The Cosmological Lithium Problem and its Probable Solutions

Transcription

1 The Cosmological Lithium Problem and its Probable Solutions Vikramdeep Singh Guru Nanak Dev University, Amritsar Adviser: Dr. Dhruba Gupta, Bose Institute, Kolkata Abstract Light elements (H, D, 3 He, 4 He, 7 Li, and 7 Be) were produced in first twenty minutes of the Universe. Big Bang Nucleosynthesis (BBN) is the tool to probe the early Universe aging 1s ~ 500s. BBN theory is based on three assumptions; General theory of relativity, a homogeneous and isotropic Universe and Standard model of Nuclear and Particle Physics. After precise determination of a number of light neutrino species (N ν ) and the lifetime of free neutron (τ n ), the only remaining parameter in BBN theory is the Baryon density (Ω b h 2 ), or equivalently the baryon-to-photon ratio (η). Observations of Cosmic Microwave Background (CMB) anisotropies on small angular scales, gives an independent measure of baryon density. Most recent observations were done by WMAP and Planck. BBN predictions for baryon density are well tested through precise measurements of cosmic temperature fluctuations. The η value determined from the CMB anisotropies is used as an input to predict the light elements abundances. Comparison with observed abundances of light elements, these BBN+CMB predicted abundances are in good agreement for H, D, and 4 He, but 7 Li as an exception. Stellar observation of 7 Li abundance from metal-poor halo stars is only one-third of the values predicted by BBN theory using CMB data. This discrepancy is the Lithium problem. This mismatch might be because of systematic errors in observed abundances, and/or uncertainties in stellar astrophysics or nuclear data, or there might be new physics at work. All of these factors are well studied, but the longstanding Li problem is yet not resolved. Origin of the problem, present status and probable solutions of the problem are discussed in this project report. Contents The Cosmological Lithium Problem and its Probable Solutions Introduction Big Bang Nucleosynthesis Origin of BBN Important nuclear channels Important parameters of BBN theory... 5 Page 1

2 3. Cosmic Microwave Background Origin of CMB CMB anisotropies Measuring cosmological parameters from CMB anisotropies Light Element Abundances Expressing nuclear abundances Predictions from BBN using CMB data Deuterium abundance (D/H) Helium-3 abundance ( 3 He/H) Helium-4 abundance (Y P) Lithium-7 abundance ( 7 Li/H) Astronomical Observations Deuterium abundance (D/H) Helium-3 abundance ( 3 He/H) Helium-4 abundance (Y P) Lithium-7 abundance ( 7 Li/H) Comparison of Light Element Abundances Concordance Li problem Probable Solutions for 7 Li Problem Astrophysical solution Nuclear solution Extended BBN reaction network Inclusion of non thermal neutrons Resonant enhancements of reaction rates Beyond standard model solutions Photon cooling X-particle model PMF model Discussion: Baryon-to-Photon Ratio Page 2

3 8. Outlook References Tables & Figures Introduction Big Bang Nucleosynthesis (BBN) is a cornerstone of modern cosmology. Its success rests on the agreement among the observationally inferred and predicted primordial values for the Deuterium and Helium abundances. WMAP measurements of Cosmic Microwave Background (CMB) radiations have precisely determined the baryon density. Using baryon density from CMB measurements as an input to BBN outputs the prediction of light element abundances. The comparison of predicted values with the values observed from the high redshift and local Universe tests the BBN theory. In particular, the latest measurements of the Deuterium abundance, (D/H) P = (2.53 ± 0.04) 10 5 [1], are in remarkable accord with BBN predictions under standard cosmological assumptions and using the baryon-to-photon ratio precisely measured via the anisotropies in the CMB as an input. However, the BBN success is not complete, the predicted value of the Lithium abundance ( 7 Li/H) BBN = (4.68 ± 0.67) [2], is significantly higher, by a factor of (2 4), than the value inferred from the atmospheres of Population II stars, ( 7 Li/H) obs = (1.6 ± 0.3) [3]. This discrepancy constitutes The cosmological Lithium Problem. The proposed solutions of this long-standing problem are categorized in three aspects; nuclear physics solution, astrophysical solutions, and solutions beyond the standard model of physics. The terms, Ω b = ρ b ρ c Hubble parameter scaled to is the fraction of critical density in baryons, ρ c = h 2 gcm 3, h is the Kms 1 Mpc 1,and η = η b η γ = η is the ratio of number density of baryons to that of photons. The number density of photon is easily calculated from the known measured CMB sky temperature. The relation between critical baryon density and the baryon-to-photon ratio is given as, Ω b = ρ b h η 2 ρ 10. crit 274 In {2} BBN theory s origin, important nuclear reactions, and its important parameters are discussed. CMB origin and its anisotropies are discussed in {3}. In {4} the observed and predicted values of light element abundances are given. Comparison of observed and calculated values are done in {5}. In {6} probable solutions of the Lithium problem are discussed in detail. A discussion over baryonto-photon ratio is done in {7}. 2. Big Bang Nucleosynthesis Big Bang Nucleosynthesis (BBN) theory developed by Russian physicist George Gamow and his student Ralph Alpher in Standard Big Bang Nucleosynthesis (SBBN) is based on three assumptions (1) gravity at the time of BBN epoch is governed by the general theory of relativity, (2) Universe is homogeneous and isotropic, (3) assuming the standard model of nuclear and particle physics. In Page 3

4 contrast of Standard BBN, we can predict the abundances of the light elements synthesized in the early Universe. 2.1 Origin of BBN BBN is sensitive to physics at epoch t~1s, T~1MeV. At higher temperatures weak interactions were in equilibrium thus fixing the neutron-to-proton ratio, n Q = e kt, where Q = (m p n m p )c 2 = MeV is the massenergy difference between neutron and proton. As temperature decreases the neutron to proton inter-conversion rate τ n p T 5, fell faster as compared to the Hubble expansion rate H g T 2. This results in breaking of chemical equilibrium. Neutron fraction at this time is 1. This ratio is 6 sensitive to H o, present value of Hubble constant and thus provides a probe of number of relativistic neutrinos. Neutron has a free lifetime of τ n = ± 0.9s before it undergoes β-decay. After freeze out the neutron were free to decay so neutron fraction further decays to 1 by the time nuclear 7 reactions began. Rates of these reactions depend upon the density of baryons. Nucleosynthesis chain begins with the formation of Deuterium by reaction p(n,γ)d. One might expect Deuterium formation begins as soon as kt < B D, where B D is the binding energy of the Deuterium. But since there are 10 9 photons for each baryon and the blackbody radiation tail of photons dissociate any Deuterium so formed. This is Deuterium bottleneck [4]. The quantity η 1 e Q kt, i.e number of photons per baryon above the Deuterium photodissociation threshold, falls below unity at T~0.1 MeV [5]. Deuterium nuclei can then begin to form without being photo-dissociated immediately. Since density is low, only twobody reactions are of importance. D(p,γ) 3 He, 3 He(D,p) 4 He. Since 4 He is the most stable bound nucleus, all neutrons bound up in forming 4 He. Heavier elements do not form because of the absence of stable nuclei with mass number 5 or 8 and second due to large Coulomb barriers for reactions. Thus leading to 4 He mass fraction simply calculated as 2( n p ) Y = (1 + n p ) 0.25 There is little sensitivity here to actual nuclear reaction rates which are however important in determining another left abundances: D and 3 He at the level of 10-5 by number relative to H and 7 Li at the level of about Important nuclear channels The nuclear physics and the rate of nuclear reactions involved in BBN have been studied and observed experimentally. There are a large number of nuclear reaction possibilities at the BBN epoch. But only a few of them have dominant effects on the light element abundances. Here, we consider only twelve such nuclear reactions (Fig. 1), ignoring all other reactions since they have a very small effect due to their diminishing cross sections. Reactions having significant influence on primordial synthesis are [6] [8], n p p(n, γ)d D(p, γ) 3 He D(d, n) 3 He D(d, p) 3 H 3 H(d, n) 4 He 3 H(α, γ) 7 Li 3 He(n, p) 3 H 3 He(d, p) 4 He 3 He(α, γ) 7 Be 7 Li(p, α) 4 He 7 Be(n, p) 7 Li Page 4

5 Neutron-proton interconversion reactions rates of reactions involved in the equilibrium are determined by standard weak interactions. The reaction rate for H(n,γ)D is obtained in the framework of Effective field theory. The cross sections for remaining ten nuclear reactions have been measured in laboratory experiments at relevant energies. 2.3 Important parameters of BBN theory Historically, BBN theory was generally taken to be a three parameter theory with results depending on the baryon density of the Universe, the neutron mean lifetime, and the number of neutrino flavors. Indeed, concordance between theory and observations for the abundances of light elements D, 3 He, 4 He, and 7 Li, was a powerful tool for obtaining the baryon density of the Universe. Over the last 20 or so years, the number of light neutrino flavors has been fixed (in the standard model of particle physics), and the neutron mean free lifetime is measured accurately enough that it is no longer a parameter for BBN theory, but rather its residual uncertainty is simply carried into an uncertainty in the predicted 4 He abundance, since it affects this abundance[5]. More recently, the baryon density has been measured to a great accuracy by WMAP satellite and value given by is Ω b h 2 = ± [9]. This corresponds to a baryon-to-photon ratio η 10 = 6.23 ± 0.17 [9]. Thus after the evaluation of η by WMAP in the light of Standard model, and working in the framework of a Friedmann-Robertson-Walker cosmology [5,10], the only inputs to the BBN theory are nuclear reaction rates (and their observed uncertainties). 3. Cosmic Microwave Background 3.1 Origin of CMB In the early age of Universe, the temperature and density were high enough that all the matter present was in the form of plasma of protons and electrons. After 380,000 years when the temperature of Universe was low enough (T~3000K) then there was a recombination of protons and electron leading to the formation of neutral Hydrogen atoms. Cosmic microwave background (CMB) is the electromagnetic radiation which carries the information of very early Universe at the time of the recombination epoch. Before the recombination epoch, electrons acted as a glue between photons and baryons through Thomson scattering and Coulomb scattering. So the cosmological plasma was acting as a tightly coupled photon-baryon fluid. After recombination photons are no longer scattered from the baryons and thus they can travel freely and the phenomenon described as photon decoupling. CMB has a thermal black body radiation spectrum at a temperature of ± K [11](Fig. 2). CMB was first predicted in 1948 by Ralph Alpher and Robert Herman and was experimentally observed by Penzias and Wilson in 1964, who shared Nobel prize in 1978 for the same work. The CMB gives a snapshot of the Universe at the time of recombination. 3.2 CMB anisotropies The anisotropy or the directional dependency of CMB may be categorized in two kinds: primary anisotropies, due to effects occurring at the time of the recombination or last scattering and before, and secondary anisotropies, due to the effects which occur after the recombination and up to present. Page 5

6 Primary anisotropies are basically due to acoustic effect, Doppler effect, gravitational redshifts and photon diffusion, these all together form a seemingly complex spectrum. Study of the spectrum gives a variety of cosmological parameters, including the baryon density, the dark matter density, cosmological constant, the Hubble constant and curvature of Universe. In the photon-baryon fluid, photon pressure resists gravitational compression of the fluid and set up the acoustic oscillations. Regions of compression and rarefaction represent hot and cold regions respectively. These primordial fluctuations grew by gravitational instability into large scale structure of Universe today. Baryons being pressure less, still contribute to the mass of photon-baryon fluid. This changes the balance between pressure and gravity. In presence of baryons, gravitational infall leads to greater compressions of the fluid in a potential well i.e. a further displacement of the oscillation zero point [12]. Since the redshift is not affected by the baryon content, this relative shift remains after the last scattering to enhance all peaks from compression over those from rarefactions. Photons also suffer gravitational redshift from climbing out of the potentials on the last scattering surface. The combination of intrinsic temperature fluctuations and gravitational redshift is the well known Sachs-Wolfe effect [13]. Diffusion damping, the coupling between electrons and photons are not perfect as one approaches the epoch of recombination since photon possess a mean free path to Compton scattering, λ c. As photons random walk through the baryons, hot and cold regions are mixed. This imperfect coupling leads to damping in the anisotropy spectrum, very small scale inhomogeneities are smoothed out. Fluctuations damp nearly exponentially as the diffusion length. The intervening effects between recombination and present can alter the anisotropy. Secondary anisotropies are basically due to gravitational effects due to metric distortions and rescattering effects from reionization. Reionization can bring an epoch in which photons and electrons are recoupled. Reionization does both, destroys primary anisotropies and produce secondary anisotropies [14]. 3.3 Measuring cosmological parameters from CMB anisotropies The first detection of the intrinsic anisotropies of the CMB, reflecting structure in the Universe at the z rec was obtained by Cosmic Background Explorer (COBE) satellite in The variations are only 1 part in 10 5, so measuring them requires extremely high sensitivity and extremely good control of systematic errors, like contamination of the signal from other sources. Since COBE there have been a number of measurements of CMB anisotropy with higher resolution and sensitivity from ground, balloons, and satellites. The state-of-art experiments are Wilkinson Microwave Anisotropy Probe (WMAP), which just completed the analysis of its 9 years data set, the Planck satellite, which is more sensitive and has higher resolution than WMAP, and the ground-based experiments South Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT), which can get to smaller angular scales because they use large telescopes. The important observables of CMB are the power spectra of temperature and polarization maps [15]. Small intrinsic adiabatic temperature fluctuations and Thompson scattering at the last scattering surface would give rise to a very slight linear polarization of CMB. CMB anisotropies are polarized in the sense that they have slightly different amplitudes when measured in orthogonal polarizations. The polarized signal is only 10% of the full signal (which is only 1 in 10 5 in the first place), and the polarization from the foreground contaminations is hard to remove, so these measurements are tough. Roughly speaking, polarization measurements doubles (or even triples) the information content of CMB anisotropies and better pins down what is causing anisotropy on a given scale. Planck satellite will significantly advance Page 6

7 polarization measurements. Current and future ground-based and balloon-based experiments can do significantly better than Planck, while a future CMB polarization satellite would provide the ultimate in sensitivity. If we specify the statistical properties of the density fluctuations present at z rec, and the matter and energy contents of Universe, then we can predict the full pattern of CMB anisotropies. Model predictions can be tested against measurements and can be used to infer the properties of primordial fluctuations and the matter and energy contents of the Universe. The interplay between gravity and pressure introduces a preferred scale, the acoustic oscillation scale, on which CMB fluctuations are strongest. Suppose that we smooth a CMB map over an angular scale θ (Any real map will automatically be smoothed at some minimum angular scale determined by the diffraction limit of the telescope used to make it, and we can subsequently smooth the map over larger scales) (Fig. 3). Then plot a histogram of the fractional temperature variations ( T/T) in the smoothed map and measure the root-mean-square width of this histogram. To characterize the structure in the map, we can plot ( T/T) rms against the smoothing scale θ [16]. The most widely used statistical measure of structure in CMB maps is the angular power spectrum, C l derived from a decomposition of the map into spherical harmonics. WMAP first year data s best fit assuming a variable spectral index was Ω b h 2 = ± which corresponds to a value of η 10 = 6.14 ± 0.25 [17]. The five-year WMAP data is consistent with their first-year data, and the errors have been significantly reduced. Five-year data gives Ω b h 2 = ± or η 10 = 6.23 ± 0.17 [18]. In using the WMAP value for η at the period of BBN, we are implicitly assuming that there has been no entropy change between BBN and the decoupling of CMB. 4. Light Element Abundances 4.1 Expressing nuclear abundances Before getting involved with predicted and observational values of the light element abundances, first clarify how to express these light elemental abundances. There are basically two ways in which abundance of a nucleus A M can be expressed. 1. As the relative ratio of the number of A M nuclei in the Universe with respect to the number of Hydrogen nuclei ( A M/H). Since Hydrogen is most abundant in the Universe this ratio will always be less than 1. Most of the light elements abundances are expressed in this fashion. It is convenient way to express element abundances, since the astronomical observations of elemental abundances are also done by comparing the absorption or emission line intensities ratio with respect to those of Hydrogen. All light element abundances are expressed in this way except Helium abundance. 2. As the fraction of mass (X M) contributed by A M nuclei in Universe to the total baryonic mass of Universe. In this expression, the abundance is expressed in the term of mass rather than the number of nuclei. In particular mass fraction of Hydrogen is expressed in terms of X and that of Helium as Y and the rest of all elements as Z, such that X + Y + Z = 1 for the Universe. Since H and 4 He are abundant in large dominance and Z is less than 1%, thus we can consider X + Y = 1. The primordial mass fraction of 4 He is expressed as Y P. Page 7

8 The abundance of nuclei A M in terms of mass fraction (X M) is correlated to the abundance value in terms of number ratio ( A M/H) and the relation between these two is given as, X M = AX ( A M/H) (m n m p ) X is the mass fraction of Hydrogen. Mass fraction of Hydrogen is around 75% and that of helium can be approximated as 25%. Using X M = 25%, we can calculate ( 4 He/H)=1/12 [19]. Mass fraction is a monotonic increasing function of number ratio, which can be taken to be almost a linear function if the variation in X is neglected. Thus, if we measure the abundance in terms of the mass fraction or in terms of number ratio then we will get different numerical values for both but the relation of the abundance of an element with η would be same in both expressions. 4.2 Predictions from BBN using CMB data Deuterium abundance (D/H) A small fraction of deuterium (D) is not processed into heavier nuclei, giving rise to small deuterium abundance. Unlike Helium-4 Deuterium abundance strongly depends upon η. With increasing η the probability for the escape of D reduces and so does its abundance. At Planck value of η, the primordial abundance of the Deuterium is (D/H) P= (2.67 ± 0.09) 10 5 [6], [20]. The error (~7%) is partly due to the uncertainty in the value of η, and partly due to BBN errors, especially D(p,γ) 3 He, p(n,γ)d and D(d,n) 3 He [7] Helium-3 abundance ( 3 He/H) A small amount of 3 He and 7 Li were also produced during primordial synthesis. Its abundance is predicted to be ( 3 He/H) P = (1.05 ± 0.03) 10 5 [20]. 3 He is a fragile nucleus, and its abundance decreases substantially with η. The error in ( 3 He/H) P (~7%) is dominated by the uncertainties in the reaction rates of D(p,γ) 3 He and 3 He(n,γ) 4 He [7] Helium-4 abundance (Y P) The reaction p(n,γ)d as well as the reactions processing D to 4 He are fast. So, almost all neutrons in the Universe go to 4 He. Consider there were p protons and n neutrons at that time in the Universe (n < p, and the ratio of neutron to proton is n p ). If all neutrons go to 4 He, then each nucleus has 2 protons and 2 neutrons. We see that out of p protons n protons go to n/2 4 He nuclei and the rest (p n) protons remain as H nuclei. Mass of one 4 He nucleus is equal to 2(m n + m p ). Therefore, taking n p = 1 7 the primordial 4 He abundance can be estimated (as done in {2.1}) as Y P 0.25 and the primordial 4 He/H ratio as 1/12. To be more precise, predicted value of 4 He is Y P = ± [20]. It is almost independent of other nuclear reaction rates, and depends weakly on the η and increases slightly with increasing η since with higher η there are more neutrons to go into 4 He. The uncertainty in η is the main contributor for uncertainty in 4 He primordial abundance [7] Lithium-7 abundance ( 7 Li/H) Another product of BBN is lithium, 7 Li. Its predicted primordial abundance is ( 7 Li/H) P= ( ) [20]. 7 Li abundance shows a dip behavior with η. During BBN, Lithium is produced directly as 7 Li at Page 8

9 small values of η, whereas for higher values of η lithium is synthesized as 7 Be, which at later stages decays to 7 Li. The uncertainty in primordial 7 Li abundance (~12%) is dominated by uncertainties in the nuclear cross sections in the particular 3 He(α, γ) 7 Be [7]. 4.3 Astronomical Observations Deuterium abundance (D/H) BBN is the only source of Deuterium. Deuterium could not be produced in any stellar nucleosynthesis because no such stellar conditions are possible in which any produced Deuterium is not destroyed by fusing into heavier nuclei. Deuterium is only destroyed in stellar nucleosynthesis. Thus any detection of Deuterium will give us a lower limit of primordial abundance and thus an upper limit of the value of η. Deuterium is observed in distant quasar absorption systems at high redshift with metallicities of the order to 0.01 solar via its isotope shifted Lyman-α absorption. At 0.01 solar, all chemical evolution models which are consistent with galactic data predict that the destruction of Deuterium is not more than 1% [21]. Thus such systems give a correct estimate of primordial Deuterium abundance. In the best measured systems, D/H shows no hint of correlation with metallicity or redshift (Fig. 4). With improved precision, the recent observation for primordial Deuterium abundance is (D/H) P = (2.53 ± 0.04) 10 5 [1] Helium-3 abundance ( 3 He/H) The evolution of 3 He after BBN is considerably more complex and model dependent. Interstellar 3 He incorporated into stars is burned to 4 He (and beyond) in hot interiors, but preserved in the cooler regions, outer layers. Stellar production of 3 He is basically from burning of H in cooler low mass stars. However, it is unclear how much of this synthesized 3 He is returned to interstellar medium and how much of it is consumed in the post-main sequence stellar evolution. 3 He cannot be used as a tool to early Universe but it can be used to check the consistency. The observed abundances from emission lines in Galactic H-II regions, where post-bbn evolution is minimum, is ( 3 He/H) P = (1.1 ± 0.2) 10 5 [22] Helium-4 abundance (Y P) Helium-4 is second most abundant nuclei in Universe after H. In the post-bbn evolution the H is burned to Helium, which leads to an increase in 4 He abundance over its primordial abundances. As with Deuterium, a 4 He plateau is observed at low metallicity. The 4 He data relevant for BBN comes from observations of low metallic extragalactic H-II regions. A correlation is found between the 4 He abundance and the metallicity, and the primordial abundance is calculated by extrapolating the available data to zero metallicity. Because of the very large number of very low metallicity observations this extrapolating sound statistically and yields and error of only 1% in Y P. To track the primordial abundance of the 4 He mass fraction, Y is plotted versus the oxygen abundances (O/H) in the H-II regions having metallicity ranging from ~1/2 to ~1/40 of solar metallicity (for a solar oxygen abundance of (O/H) ). At sufficiently low metallicity the Y versus (O/H) relation approaches a 4 He plateau. Since Y increases with (O/H), this relation may be extrapolated to zero metallicity. Recent measurements have given the primordial helium mass fraction as Y P = ( ± ) [23]. Page 9

10 4.3.4 Lithium-7 abundance ( 7 Li/H) Lithium-7 is fragile and burn in stars at relatively lower temperatures, thus the majority of Lithium cycled through stars is destroyed. For the same reason, it is difficult that any synthesized Lithium in the stellar evolution pass to interstellar medium before it is destroyed by nuclear burning. In addition to stellar Nucleosynthesis, intermediate mass nuclei are also synthesized in cosmic ray nucleosynthesis either by α-α fusion reactions or spallation reactions due to collisions between protons and α particles and CNO nuclei. In the early Universe, when the metallicity of Universe was low enough, the post-bbn production of Lithium is expected to be subdominant to that from its BBN abundance. The Lithium observed in the atmospheres of cool, metal-poor, Population II halo stars are the most relevant for determining the BBN 7 Li abundance. Uncertainties are due to Lithium equivalent width measurements, due to temperature scales for these metal-poor stars, and their model atmosphere. Lithium is found to have a nearly constant abundance independent of metallicity for [Fe/H] < 1.3 [24]. This remarkable constancy with metallicity observed by Spite & Spite is known as Spite plateau (Fig. 5). The Lithium plateau is generally regarded to represent the primordial abundance of 7 Li and is of key importance to the understanding of BBN. Spite & Spite had found a value of 7 Li/H (1.12 ± 0.38) [24]. The more recent observations found out 7 Li/H = (1.58 ± 0.31) [23]. The metal-poor halo stars that define the primordial abundance of Li are very old. As a result, they have had time to disturb the primordial abundances that have survived in their outer, cooler layers. The mixing of this cooler layer with hot interior layer will dilute or destroy the outer layer Lithium abundance. This uncertainty is also considered in inferring primordial Li abundance. 5. Comparison of Light Element Abundances Based on theoretical and experimental inputs, the abundances of light elements have been plotted as a function of baryon-to-photon ratio, η (Fig. 6). The uncertainties in the curves are derived from uncertainties by Monte-Carlo method [7]. Once η is known primordial abundances can be calculated. 5.1 Concordance The predictions for D and 4 He abundances are in broad quantitative agreement with the measured primordial light element abundances derived from observations in the local and high redshift Universe. This concordance represents a big success of the hot big bang cosmology and makes BBN our earliest reliable probe of the Universe. For standard BBN the value of baryon density (η 10 ), inferred from the Deuterium abundance (D/H ), is η 10 = and the corresponding value of critical baryon density is, Ω b h = [22]. This is in an outstanding agreement with the value largely based on the new CMB WMAP data, which predicts Ω b h 2 = ± [9]. For baryon density determined from Deuterium abundances, the SBBN predicted the abundance of Heliuum-3 is, 3 He/H = 1.0 ± 0.1 [22], which compared to the observed value 3 He/H = (1.1 ± 0.2) 10 5 [22] is suggested to be nearly primordial. Again, this is in an excellent agreement. The quality of comparison of the predicted Helium mass fraction Y P and primordial D abundance with observations mostly depend upon the errors in extracting the primordial fractions for these elements from observation data. Fig. 7 shows the likelihood of the theory and the observations for light element abundances. Page 10

11 5.2 Li problem As shown in Fig. 6, stellar Li/H measurements are inconsistent with the CMB (and D/H) determinations. Recent updates on nuclear reaction rates and stellar abundances systematics have increased this discrepancy. The predictions are substantially higher than the observations. Depending on the treatment of systematic errors in the measured 7 Li/H, the discrepancy is a factor of ( ) [25]. This substantial mismatch constitutes the cosmological Lithium problem. Although it can be argued that some 7 Li would be destroyed by stars in which it is observed, it has been found very difficult to justify enough destruction to bring theory and observation into the agreement. Another interesting twist to Lithium story is added by the claim of the detection of 6 Li metallicity plateau at 6 Li/H ~ O(10 11 ) level, which almost certainly implies some form of pre-galactic 6 Li [26]. The significant presence of 6 Li would also have serious implications for any stellar mechanism that is able to deplete 7 Li, as 6 Li is more fragile and is destroyed at lower temperatures as compared to 7 Li. The status of 6 Li plateau claim so far remains in doubt, as a subsequent more conservative analysis found no evidence for the plateau. 6. Probable Solutions for 7 Li Problem 6.1 Astrophysical solution First, consider that standard nuclear and particle physics are correct to explain BBN and the nuclear reaction rates are correctly measured, thus the predictions of 7 Li/H from BBN are correct. If so, then the observational values of the Lithium must be in error to address the Lithium problem. Lithium abundances are measured from the observations of 7 Li absorption lines in the atmospheres of metalpoor halo stars, as a function of metallicity. 7 Li exhibit remarkable consistency with the metallicity, known as Spite plateau. Extrapolation of Spite plateau to zero metallicity is believed to reflect the primordial value of 7 Li. If misstep exists in this reasoning then the Lithium problem may be alleviated. What observed is total abundance of the Li, summed over all of its ionization states. However, the 670.8nm line is sensitive only to Lithium in its neutral ground state. However in most of the stars due to high temperature Lithium is mostly singly ionized. Thus, it needs to bring ionization correction which is exponentially dependent on the stellar temperature [25]. Thus a systematic shift upward in stellar temperature scale of halo stars would increase all stellar Lithium abundances and raise the Spite plateau towards WMAP+BBN prediction. However, accurate determination of the stellar temperature remains non-trivial since these emergent radiations do not have perfect black body radiation spectrum nor local thermal equilibrium is completely attained in these stellar environments. However, later detailed studies of stellar temperatures are in good agreement with the old temperature scale, leaving the Lithium problem unresolved. The other question which arises is whether the observed abundances are the primordial ones. It might be possible that during the age of Universe, Lithium is destroyed in the halo stars and thus what we observe today is a lower limit of the primordial abundance. Due to the lower binding energy of 7 Li, it is destroyed at a temperature of few million Kelvin (~ K) [25]. It needs to be exposed to relatively low stellar temperatures to suffer substantial destruction over the lifespan of halo star. The major effect for destruction is convection which circulates photospheric material deep into the interior where nuclear burning can occur. There are many other mixing effects Page 11

12 which can deplete the photospheric 7 Li abundances such as turbulence, rotational circulation, diffusion and internal gravitational waves and gravitational settling. The presence of 6 Li limits these mixing models for depletion of 7 Li by a big factor. Since, 6 Li is more fragile than 7 Li and burn down at T~ K, thus if the stellar photospheric matter was exposed to temperatures hot enough to burn 7 Li then the 6 Li should be completely destroyed which is contrary to observations. Several groups found out that at low metallicity the 7 Li abundance on average falls below the Spite plateau [27]. At low metallicity, there is star to star scattering of 7 Li abundances which confirm the depletion of Lithium over time in some of the halo stars. However, no significant scatter is observed which can account for Lithium problem. The astrophysical solution of the 7 Li problem is not yet found and other solutions need to be considered. 6.2 Nuclear solution Nuclear physics solutions are considered under the assumption that the observed abundances are the primordial ones and there are no objections on observed values, and the standard model of nuclear and particle physics are valid to explain things at the BBN epoch. Nuclear solutions basically consider the study of reaction rates of additional nuclear reactions to the BBN reaction network, nonthermal neutron reaction rates, and resonant enhancements of reactions Extended BBN reaction network Some reactions which are naturally a part of BBN network but were not considered earlier. In most of the cases either the target, or beam, or in some cases both nuclei are unstable and radioactive which make experimentation with these nuclei much difficult. It seems appropriate to reexamine the BBN network to be sure that all possible reactions are included and to study the potential effects of those reactions for which data do not exist. The extended BBN reaction network is shown in (Fig. 8). Mass 7 is made primarily as 7 Be at the WMAP baryonic density. Candidate reactions for the destruction of mass 7 include 7 Be( 3 H, 4 He) 6 Li. Another reaction of particular interest for synthesizing 6 Li is 3 He( 3 H,γ) 6 Li. Deuteron capture are reactions that can have an appreciable effect on abundances of 6 Li and 7 Be. The reaction rate for 7 Li( 3 H,n) 9 Be was found to proceed to both 9 Be ground state and the excited state [28]. Since the rate to the ground state is times the rate of the continuum state, destruction of 7 Li is more likely than the production of 9 Be by this reaction. 7 Be(p,γ) 8 B, 7 Be(d,p) 8 Be and 7 Be( 3 H,n) 9 B all of which create nuclei that undergo particle decay and so result in the destruction of 7 Be. Another reaction of particular interest is 3 He( 3 H,γ) 6 Li, has a large positive Q value ( MeV) which can go to many excited states of 6 Li. The 6 Li ground state is stable, the second excited state decays to the ground state and all other states undergo breakup to 4 He + 2 H. Thus this reaction can produce 6 Li. Added nuclear reactions to the BBN network with their effect are shown in (Table 1). It can be concluded that the added reactions have a very slight effect on the BBN abundances. Only 7 Be( 2 H, 3 He) 6 Li reaction produced a large effect to suggest that it might be important in destroying 7 Be ultimately resulting from BBN. It reduces the mass 7 abundance by 30%, however, that required a factor of 1000 increase in reaction rates, which is well outside the expected uncertainties in the nuclear reaction rates. Of some interest, was the inclusion of 6 He in reaction networks. This species is converted quickly to 6 Li by weak interactions. 6 Li(p, 4 He) 3 He has the largest effect in 6 Li destruction mainly because of the large abundance of protons when 6 Li was created [28]. Page 12

13 6.2.2 Inclusion of non thermal neutrons Another aspect of BBN that we study is the inclusion of nonthermal particles. It has generally been assumed that BBN reactions occur in such an environment where ions have thermal, Maxwellian velocity distributions. This approximation could be violated at some levels by reactions induced by highly energetic exothermic reactions. Most likely scenario for this process involves neutron produced in 3 H(d,n) 4 He and proton induced in 3 He(d,p) 4 He. These reactions include the entrance channel present in large abundances and thus have large cross sections and produce nuclei with energies in excess of 10MeV [29]. Recent work showed that thermalization of charged nonthermal particles take place rapidly through the electromagnetic process so that these charged particles are of less interest and have a small negligible effect on BBN abundances. However, that study investigated only charged nonthermal particles but did not consider the thermalization of the neutron which occurs over a large time scale compared with those of proton. It might be thought that the nonthermal neutrons can affect the BBN abundances, specifically that of 7 Be, through 3 He(n,p) 3 H and through neutron induced reactions of 7 Be. The former reaction could reduce the abundance of the 7 Be after it is produced in BBN and the reaction 7 Be(n, 2 H) 6 Li which is endothermic could produce 6 Li. The thermal neutrons produced by 3 H(d,n) 4 He in BBN, they lose energy and eventually thermalize on scattering with the other nuclei. If it is assumed that the time in the BBN is late enough that scattering from other neutrons can be ignored, the most significant scattering source is 1 H, proton nuclei, which is lightest nuclei and makes up over 90% of the number density at BBN. The only other relevant nuclei present is 4 He, has a neutron scattering cross section 30% that of the 1 H cross section, but contribute less than 10% of the total number density and is also less favorable for energy transfer due to its larger mass [30]. Thus we only consider energy losses from 1 H. Our ultimate goal is to find out the nuclear reactions it undergoes before thermalization. The energy transfer from nonthermal neutrons to the target nuclei depend upon the scattering angle. Assuming, the differential scattering cross section to be uniform in every direction, i.e. isotropic in the center of mass frame, assuming neutron-proton mass nearly equal, and considering non-relativistic kinematics are applicable, the energy loss by a neutron due to single scattering is uniformly distributed from zero to maximum energy of the neutron. These conditions are satisfied within a few percent below 20 MeV for neutrons. The important reaction with non thermal neutrons, which have a considerable effect on the BBN abundances are, D(n,p)n which leads to the destruction of the Deuterium, however, this reaction occurs only when the formation of 4 He begins. The other reaction is 3 He(n,p) 3 H, this reaction is exothermic and can also proceed via thermal neutrons. This reaction depletes 3 He which is the source of 7 Be. However, the effect on BBN abundances is found to be of the order of 10-4 or even less, much smaller than the level of uncertainties arising from other sources such as reaction rates [29] Resonant enhancements of reaction rates We need to investigate whether resonant enhancement of 7 Be burning reactions may solve the 7 Li problem by reducing the primordial source of 7 Li. The enhancement of nuclear reaction rates by nuclear resonances is extremely important in nuclear astrophysics. 7 Be is the source of 7 Li at BBN η value, the main production reaction for 7 Li is, 3 He(α, γ) 7 Be and the destruction reactions of mass-7 are 7 Be(n,p) 7 Li, 7 Li(p,α) 4 He. The other parameters that regulate the 7 Be abundances are the availability of free neutrons and α particle which in turn depends upon the reaction rates for elements with a mass number less than 4. The narrow resonances may modify reactions between light elements and affect the abundances of Page 13

14 3 He and neutrons at T~40keV that directly affects the outcomes of the 7 Be and 7 Li abundances. Only those resonances which have resonance energies of the order of 300keV or so are considered so that they are important at BBN energies [31]. All the primary reactions at the BBN energies are very well known, both theoretically and experimentally, and no big changes in their rates within the realm of standard BBN are possible. The search for resonances must be done in the secondary BBN reactions. There are direct reactions of burning of 7 Be by light elements other than n, such as p, D, 3 H, 3 He and α particle, which therefore should involve resonances in elements as 9 B and 11 C. Resonances in 11 C cannot play any role in the depletion of 7 Be since it has very narrow resonance. The 16.7MeV 5/2 + resonance in 9 B has more substantial hope for reducing the 7 Be and being just ~200keV above the 7 Be+D threshold, may lead to the resonant enhancement of 7 Be(d,p)2α and 7 Be(d,γ) 9 B reactions [31]. This resonance may be very strong, and at the very limit of the quantum mechanically allowed value for the deuteron separation width, which would be responsible for a factor of 2 suppression of the primordial 7 Be yield, thus resolving the Lithium problem. This resonance is presumably somewhat below the range of energies probed by experiment [32] and due to a non-monotonic dependence of S-factor on energy, could have been missed. The possibility of having a resonance with Г < T is important, as it leads to a significant variation of astrophysical factor S(E) in the relevant energy range. We find the very fact that there exists a possibility for nuclear physics solution via 7 Be+d reaction resonance enhancement. The work done for remeasuring the reaction rate for 7 Be(d,p)2α there was an explicit assumption made that S(E) is a smooth function of energy below 400keV. This assumption is violated by 16.7MeV resonance. The decay of 16.7MeV state of 9 B may proceed to 8 Be 16.63MeV level which proceeds to decay into 2α. There are also other possible final states such as 6 Li+ 3 He and 9 B+γ. If we go for other possibilities 7 Be+ 3 H, we shall discover no matter what the properties of 2+ resonance in 10 B are, it cannot lead to an appreciable depletion of 7 Be since tritium is much less abundant than the Deuterium abundance at relevant temperature [27]. An experiment is proposed for the search of higher excitation states of 8 Be * up to about 20MeV [33]. The contributions from higher excited states were negligible in experiment [32] which was performed at lower energies. The proposed experiment at a much higher energy of 35MeV may throw light on the breakup channels of 8 Be into 6 Li+D and 7 Li+p, and would also search for 16.7MeV resonance state of 9 B. These future efforts might either support this hypothesis thus offer a nuclear physics solution to the Lithium problem, or refute it, closing perhaps the last nuclear loophole in the BBN prediction of Lithium abundance. 6.3 Beyond standard model solutions New physics solutions or the solutions beyond the standard model are considered in the realm that the observed abundances are the primordial ones with minimum uncertainties and that the nuclear physics behind BBN is correct i.e. there is no hidden uncertainty in nuclear reaction rates. Such proposed solutions include time-varying fundamental constants, which in turn affects the binding energy of the Deuterium and thus affecting the whole BBN, or using nonstandard cosmologies in which the Universe is not homogeneous at Hubble s scale. These solutions are somewhat speculative. We are considering here three proposed cosmological beyond the standard model solutions. Page 14

15 6.3.1 Photon cooling We assume the photon cooling occurred after the BBN and before the photon decoupling. If the photons were cooled sometime after the BBN and before the recombination, then the baryon to photon ratio (η) during the BBN would be small as compared to its present value, and thus the excess production of Li during BBN can be avoided. The candidate particles involved in such a mechanism are a possible scalar particle that forms a Bose-Einstein Condensate (BEC) during the post-bbn epoch, but before photon decoupling during recombination epoch. Due to photon cooling, the number density of photons is greater than without it. Therefore, the baryon-to-photon ratio during BBN epoch η BBN would be smaller than its present value fixed by the CMB power spectrum. In photon cooling model the abundance of D, 3 He, and 6 Li increases, while the abundance of 4 He and 7 Li decreases. The 7 Li abundance considering photon cooling model might be consistent with the observed values and can solve Lithium problem [29]. However, the predicted abundance of D is much higher and inconsistent with the observed value. Photon cooling model taken along with the X-particle decay model can solve the Lithium problem X-particle model Another beyond the standard model proposed solution for Lithium problem is the radiative decay of hypothetical long-lived exotic massive particle (X) after the BBN. This model cannot solve the Lithium problem itself but it can solve the overabundance of D in the photon cooling model. In a hybrid model, consisting of photon cooling and X-particle decay the primordial D abundance is reduced by photodisintegration of D by nonthermal photons injected by the radiative decay of long-lived X-particle. As the temperature of the Universe decreases these nonthermal photons disintegrate the light elements synthesized in the BBN. Among these light elements, D and 7 Be are most strongly photodisintegrated. They are mainly photodisintegrated via 7 Be + γ 3 He + 4 He and D(γ,n)H reactions where γ s are nonthermal photons. Long after BBN epoch the 7 Be nuclei capture an electron and converted to 7 Li, thus the total primordial abundance of the 7 Li is the sum of abundances of 7 Li and 7 Be produced in BBN. Photodisintegration of 7 Be by the decay of X particle thus reduces the primordial 7 Li abundance. The problem of overabundance of D in photon cooling model is solved considering X-particle decay model since D is also photodisintegrated due to nonthermal photons and thus reducing its primordial abundance. Another probable solution for the 7 Li problem is based upon exotic atomic and nuclear reactions induced by a long-lived exotic massive charged particle X during BBN. Such a charged particle of mass m X O(1GeV) can recombine with positively charged nuclei via radiative capture of bare nuclei and X particle or nuclear charge-exchange reactions between electronic ions and X particles, especially 7 Be 3+ + X 7 Be X + e in a late epoch of BBN. Bound states of nuclei and X i.e. A X or X nuclei, then induce atomic and nuclear reactions. Among the reactions, new type of resonant nuclear reactions of 7 Be X + p 8 B X + γ are made possible through an atomic excited state, 8 B X a and an atomic ground state consisting of the 1 + nuclear excited state of 8 B and an X i.e. 8 B * (1 +,0.770MeV) X [29]. Primordial abundance of 7 Be is destroyed via these reactions and the final abundance ratio of 7 Li/H is reduced. Although this remains as an interesting solution to the 7 Li problem, the destruction of Deuterium does not occur in this model. Page 15

16 6.3.3 PMF model A third cosmological solution for the Lithium problem is the Primordial Magnetic Field (PMF) model. BBN with PMF leads to different results than without a PMF and can potentially improve the solution of Lithium problem. The expansion rate of the early Universe at the BBN epoch depends upon the energy densities. When one adds the energy density of the PMF to the radiation energy density then the cosmic expansion rate of the Universe at the BBN epoch is more rapid. Due to high expansion rate, the freeze out of the weak interactions between baryons occurs earlier, which leads to an increase in the neutron to proton ratio. Thus, the neutron abundance at the epoch of weak interactions freeze-out increases. Due to high expansion rate, the time interval after the freeze out until the production of 4 He nuclei also decreases. Therefore, more neutrons can undergo nucleosynthesis, since more neutrons survive the βdecay due to short time interval [29]. Thus the abundance of 4 He increases significantly, while the abundance of D and 3 He increases moderately, the abundance of 6 Li increases slightly, and the 7 Li abundance decreases. Thus the primordial 7 Li starts to cooperate with the observed values after taking PMF into consideration. 7. Discussion: Baryon-to-Photon Ratio Baryon-to-photon density (η) is related to universal critical baryon density (Ω b h 2 ) as, η 10 = 274Ω b h 2. The predictions of abundances of light elements synthesized in the early Universe are strongly dependent upon the matter content of the Universe mainly through baryon-to-photon ratio at that time. This ratio can not be measured experimentally. Before the era of precise measurement of CMB anisotropies, a measurement of this ratio is done by observing the primordial abundances of the light elements in Universe. Any ratio of two primordial abundances gives a value of η and hence Ω b h 2. Since Deuterium is synthesized only in the BBN thus any observation of the D abundances would give an upper limit value of η. Deuterium abundances observed from distant quasar absorbing systems gave a higher confidence upper limit, the value of η < [34], but a reliable lower limit to η, much less a precise value has been problematic. Using combined 4 He, 7 Li and D abundances enable one to determine a 95% CL range of 5.1 < η 10 < 6.7 with a most likely value of η 10 = 5.7 and corresponding Ω b h 2 = [4]. However, one might concerns regarding the likelihood method is a relatively poor agreement between 4 He and 7 Li on one hand and D on the other. The former two taken alone indicate the most likely value for η 10 is 2.4, while D/H alone implies the best value of 6.1 [34]. With the advent of observations of CMB anisotropies from ground-based, balloon-based and satellite observations, an independent measurement of η 10 become possible. The assumption behind this is that the value of η 10 had not changed between the post-bbn and the recombination epoch. The value of η 10 which we observe today from CMB anisotropies is same as the value at the time of BBN. CMB based inference of the baryon-to-photon ratio is η 10 = 6.14 ± 0.25 and corresponding Ω b h 2 = ± [17]. Primordial abundances of the 4 He are almost insensitive to the baryon density very slightly depending on η, but since all neutrons available at the BBN are incorporated in 4 He, Y P does depend upon the composition between the weak reaction rates and the Universal expansion rate. The higher nucleon density, earlier the deuteron bottleneck be breached. Since at early stages there are more neutrons as fraction of nucleons, more 4 He will be synthesized. This latter effect is responsible for a very slow Page 16

17 increase in Y P with η, as can be seen in (Fig. 6). The abundance of D decreases with higher values η since more the nucleon density more will be the possibility of synthesizing 4 He nucleus due to its strong binding as compared to the D synthesis which is the loosely bound nucleus. The higher the baryon density faster the primordial D is destroyed, so the relic abundance of D is anticorrelated to η. The 7 Li abundance strongly depends on the value of η. There are two main channels for 7 Li production. At low values of the η 10 < 3 mass-7 is largely synthesized as 7 Li via 3 H(α, γ) 7 Li reaction which is easily destroyed in collisions with protons. So with increasing value of η, the destruction of synthesized 7 Li becomes faster and thus the abundance of 7 Li decreases. At relatively higher values of η 10 > 3, mass-7 is largely synthesized as 7 Be via reaction 3 He(α, γ) 7 Be which is more tightly bound as compared to the 7 Li nucleus and therefore harder to destroy because of higher Coulomb barrier. As η increases at high values, the abundance of the 7 Be increases. Later in the evolution of the Universe, when it is cooler and neutral atoms begin to form, the 7 Be nucleus will capture an electron and undergoes β- decay to 7 Li. From (Fig. 6) for a lower value of η, the predicted and the observed value of the 7 Li abundance is in consistency. But for this lower value of η, the D abundance is much higher than the predicted one, thus shifting the problem from the Lithium to Deuterium. The observations of D abundances are done in distant quasar absorption systems with very low metallicity such that the depletion of D is very small in these systems and thus the observed abundances are the primordial one. Thus there is no discrepancy regarding the D observations. The value of η inferred from CMB anisotropies is measured very precisely first by WMAP and then by Planck. This value of η is in agreement with the value of η determined from BBN theory using D abundances. Such a consistent value of η from two completely independent measurements, assure than the value of η inferred from CMB anisotropies is correct. There are proposed models for solving Li problem which considers a shift in the value of η. One such model considers the value of η to be different in local observation systems as compared to the distant ones due to inhomogeneous Universe. Another proposed model is photon cooling, explained in {6.3.1}. However, all these models are only probable solutions. 8. Outlook We discussed the BBN and the predictions of the light element abundances from BBN, CMB anisotropies and measurement of η from it. Comparison of the light element abundances from theory predictions with observations is done. The cosmological 7 Li problem and its probable solutions are discussed. No perfect solution of the 7 Li problem has yet been found. It is to emphasize here, that the search for the origin of the 7 Li discrepancy is extremely important for the consistency of modern cosmology. It may hold a clue for the modification of the standard cosmological framework, or at the very least lead to a new level of understanding of physical processes in stellar atmospheres. References [1] R. Cooke, M. Pettini, R. A. Jorgenson, M. T. Murphy, and C. C. Steidel, Precision measures of the primordial abundance of deuterium. Page 17

18 [2] R. H. Cyburt, B. D. Fields, K. A. Olive, and T.-H. Yeh, Big Bang Nucleosynthesis: 2015 Rev. Mod. Phys., vol. 88, April, [3] A. Goudelis, M. Pospelov, and J. Pradler, Light Particle Solution to the Cosmic Lithium Problem, Phys. Rev. Lett., [4] S. Sarkar, Measuring the baryon content of the universe : BBN vs CMB. [5] R. H. Cyburt, B. D. Fields, and K. A. Olive, An update on the big bang nucleosynthesis prediction for 7 Li: the problem worsens, J. Cosmol. Astropart. Phys., [6] A. Coc, J.-P. Uzan, and E. Vangioni, Standard big bang nucleosynthesis and primordial CNO Abundances after Planck, [7] A. Coc and E. Vangioni, Big-Bang nucleosynthesis with updated nuclear data, J. Phys. Conf. Ser., vol. 202, [8] A. Coc, E. Vangioni-Flam, P. Descouvemont, A. Adahchour, and C. Angulo, Updated Big Bang Nucleosynthesis confronted to WMAP observations and to the Abundance of Light Elements, [9] C. L. Bennett et al., Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results, pp , [10] D. Baumann, Cosmology, Unpublished. [11] D. J. Fixsen, The Temperature of the Cosmic Microwave Background, Apj, vol. 707, pp , [12] W. Hu and S. Dodelson, Cosmic Microwave Background Anisotropies, [13] M. Ahlers and P. Mertsch, Origin of small-scale anisotropies in Galactic cosmic rays, Prog. Part. Nucl. Phys., vol. 94, pp , [14] W. Hu, N. Sugiyama, and J. Silk, The Physics of Microwave Background Anisotropies, [15] W. Hu, CMB Temperature and Polarization Anisotropy Fundamentals, [16] Cosmology lecture notes. [17] G. Hinshaw et al., First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing Methods and Systematic Errors Limits, [18] C. Bennett et al., First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission, [19] A. Weiss, Elements of the past: Big Bang Nucleosynthesis and observation, Einstein Online, vol. Page 18

19 2, [20] F. O. C. France, Standard Big-Bang Nucleosynthesis after Planck, [21] J. M. O. Meara et al., The Deuterium to Hydrogen Abundance Ratio Towards a Fourth QSO: HS ,. [22] G. Steigman, Big Bang Nucleosynthesis : Probing the First 20 Minutes, [23] a Coc, J. Uzan, and E. Vangioni, Standard Big-Bang Nucleosynthesis after Planck, arxiv Prepr., no. 2010, [24] F. Spite and M. Spite, Abudance of Li in Unevolved Halo Stars and Old Disk Stars: Interpreation and Consequences, Astron. Astrophys., vol. 115, [25] B. D. Fields, The Primordial Lithium Problem, [26] E. Vangioni-Flam, M. Cassé, R. Cayrel, J. Audouze, M. Spite, and F. Spite, Lithium-6: evolution from Big Bang to present, New Astron., [27] J. C. Howk, N. Lehner, B. D. Fields, and G. J. Mathews, Observation of interstellar lithium in the low-metallicity Small Magellanic Cloud, Nature, vol. 489, [28] R. N. Boyd, C. R. Brune, G. M. Fuller, and C. J. Smith, New Nuclear Physics for Big Bang Nucleosynthesis, [29] D. G. Yamazaki, M. Kusakabe, T. Kajino, and M. Cheoun, Cosmological solutions to the Lithium problem: Big-bang nucleosynthesis with photon cooling, X -particle decay and a primordial magnetic field, [30] M. Kang, Y. Hu, and H. Hu, Cosmic Rays during BBN as Origin of Lithium Problem,, [31] R. H. Cyburt and M. Pospelov, Resonant enhancement of nuclear reactions as a possible solution to the cosmological lithium problem, June [32] T. A. Journal et al., A. Coc, J. Kiener, and V. Tatischeff, [33] N. T. Committee et al., Search for higher excited states of 8 Be* to study the cosmological 7 Li problem, [34] S. Burles, K. M. Nollett, and M. S. Turner, What is the big-bang-nucleosynthesis prediction for the baryon density and how reliable is it?, Phys. Rev. D, vol. 63, [35] R. Cooke, M. Pettini, K. M. Nollett, and R. Jorgenson, The primordial deuterium abundance of the most metal-poor damped Lyman-alpha system, Astrophys. J., vol. 830, [36] S. Riemer-Sørensen et al., A robust deuterium abundance; re-measurement of the z = absorption system towards the quasar PKS , Mon. Not. R. Astron. Soc., vol. 447, Page 19

20 Tables & Figures Figure 1: A simplified nuclear reaction network of BBN including all 12 most important BBN reactions. This diagram also represents the nuclear reactions leading to 7 Li production. (Reproduced from Ref.[2]) {Back to {2.2}} Figure 2: Blackbody radiation spectrum of Cosmic Microwave Anisotropy. On horizontal axis, frequency in cm -1 and on vertical axis Intensity of the radiation is represented. (Reproduced from Ref[11]) {Back to {3.1}} Figure 3: Sky map of Cosmic Microwave Background based on WMAP observations. (Reproduced from Ref.[9]) {Back to {3.3}} Page 20

21 Figure 4: D/H observations, as a function of metallicity, blue circles indicating results from [35] and red squares indicating results from[36]. These most recent observations have very small error bars and show very small dispersion, and are just slightly below BBN calculations. (Reproduced from Ref.[20]) {Back to {4.3.1}} Figure 5: A compilation of the Lithium abundance data as a function of metallicity from stellar observations. ϵ(li) (Li/H), and [Fe/H] is the usual logarithmic metallicity relative to solar. Note the Spite plateau in Li/H for [Fe/H] 2. (Reproduced from Ref.[25]) {Back to {4.3.4}} Page 21

22 Figure 6: (Color online) Abundance of D, 3 He, 4 He and 7 Li (blue) as a function of baryon-to-photon ratio (η) (bottom) or critical baryon density (Ω b h 2 ) (top). The vertical areas correspond to WMAP (dot, black) and Planck (solid, yellow) baryonic densities, while the horizontal areas (green) represent the observational abundances. The red dotted lines correspond to the extreme values of the effective neutrino families coming from CMB Planck study, N eff = (3.02, 3.70). (Reproduced from Ref.[23]) {Back to {5}} Figure 7: Comparison of calculated and observed abundances of the light elements ( 4 He, D, 3 He, 7 Li). Blue curves show abundances predicted from the BBN and the yellow curves show the observational abundances, with dotted and dashed lines showing different analysis of observational data. (Reproduced from Ref.[25]) {Back to {5.1}} Page 22