Inflation from High Energy Physics and non-gaussianities. Hassan Firouzjahi. IPM, Tehran. Celebrating DBI in the Sky.

Transcription

1 Inflation from High Energy Physics and non-gaussianities Hassan Firouzjahi IPM, Tehran Celebrating DBI in the Sky 31 Farvardin 1391

2 Outline Motivation for Inflation from High Energy Physics Review of String Theory Brane Inflation DBI Inflation Conclusion

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4 Motivation for String Cosmology Recent observations strongly support inflation as the origin of big bang and the structure formation in universe. However, the origin of the inflation is not known from a fundamental theory point of view. String theory, on the other hand, is a consistent theory of quantum gravity. Furthermore it is expected to provide a framework for a unified theory. So far String theory did not make direct contact with observations. Since the scale of inflation is very high, possibly GUT scale, it is natural to expect that string theory was relevant in driving inflation. This would provide a unique chance to test the relevance of string theory to the real world.

5 Inflation in the context of ever changing fundamental theory inflation Old Inflation Lev Kofman New Inflation Chaotic inflation SUGRA inflation 1990 Double Inflation Power-law inflation Hybrid inflation Extended inflation SUSY F-term inflation SUSY D-term inflation Assisted inflation Brane inflation 2000 SUSY P-term inflation N-flation Super-natural Inflation K-flation inflation Racetrack inflation Tachyon inflation DBI inflation Matrix-inflation Warped Brane inflation

6 Slow Roll Inflation In most models, inflation is derived by a scalar field, the inflaton. This creates a negative pressure required for acceleration. For a scalar field ρ = 1 2 φ 2 + V (φ) p = 1 2 φ 2 V (φ) a(t) e H t, H 2 = 8πG 3 V Baumann.

7 Predictions of slow roll inflation 1-The quantum fluctuations from the inflaton field source the curvature perturbation R Ḣ φ δφ 2- The perturbations are almost scale invariant, almost Gaussian and almost adiabatic ( R k R k = 1 ( ) H 2k 3 δ3 (k + k 2 2 ) φ P R 10 9 k n s 1 3- There would be tensor perturbations with the relative amplitude r < The level of non-gaussianity is given by parameter fnl

8 All Known particles are low-lying string vibrations. String theory is a consistent theory of quantum gravity. All interactions consist of the splitting and joining of these elementary strings: In string theory, gauge fields (photons) are given by open strings while graviton is represented by closed strings. Originally it was a theory of strings but subsequent developments showed that that it also contains higher dimensional defects, D-branes. Photons are confined to the branes, representing the Standard Model Particle Physics while graviton, the closed string modes, propagate to the bulk.

9 The Brane World Scenario In brane world picture, we (the Standard Model particle physics) are confined to a D3-brane, a threedimensional hyper-surface in a higher dimensional space-time. The D3-brane spans our entire Universe. The gravity can propagate in the extra dimensions, bulk. This can explain why gravity is so weak compared to electro magnetic interactions. Force laws fall faster in higher dimensions because there are more rooms for gravity to escape. For example in 4+n space-time: If n=2, then the size of the extra dimensions can be as large as 0.01 mm! This is within the reach of the current table-top experiments.

10 Moduli In String Theory String theory is a higher dimensional theory. After compactification to four dimensions one gets many scalar fields, moduli, depending on details of compactifications. Good News: Due to large number of moduli, it is possible that some of them play the role of inflaton field. Examples are: Tachyon Inflation, Racetrack Inflation, DBI-Inflation, D3-D7 Inflation, Brane Inflation, Warped Brane Inflation. In general, the inflaton field is either an open string mode(brane position) or a closed string mode (complex Kahler moduli). Bad News: These moduli may couple to the inflaton field and interfere with the slow roll conditions. Furthermore, If they are not stabilized they will destroy the success of late time big bang cosmology, like big bang nucleosynthesis. The first task in string cosmology is the understanding of moduli and their stabilization mechanism.

11 Brane Inflation G. Dvali and H. Tye, hep-ph/ In brane inflation the inflaton field is the distance between brane and anti-brane. There is an attractive force between brane and anti-brane. If the potential is flat enough one can get enough inflation. When the distance between brane and anti-brane is at the order of string scale, a tachyon develops. Inflation ends when brane and anti-brane collide. Problem: In flat CY, the potential is too strong to achieve the slow-roll conditions for inflation. brane anti-brane

12 Problem with the Original Brane Inflation L The potential between D3 and anti-d3 branes is r The where r is the distance between them in extra dimensions. In terms of canonically normalized field the potential is To have slow-roll inflation one requires that where Noting that where L is the typical size of extra dimension yields Hence is possible only for r > L which is a contradiction!

13 Warped Brane Inflation KKLMMT: hep-th/ ) The background geometry is locally an AdS where N is the background charges(branes). The action is where the local action is with The local action becomes

14 In the slow-roll limit the gravitational attraction and the RR repulsion of D3-branes forces cancel out and and On the other hand for the anti-d3 branes, both forces are attractive and the anti brane is attracted towards the bottom of the throat with potential Once the anti-brane is at the bottom of the throat it attracts the D3-branes with the Coulombic potential The total potential of the system is

15 DBI brane inflation Alishahiha, Silverstein, Tong, hep-th/ The action of mobile D3-brane (inflaton field) is where considerations from the throat geometry and AdS/CFT Now the cosmological evolutions are given by The energy density and the pressure are Here is the Lorentz factor Pindicating the ultra-relativistic motion of the brane: γ = 1 1 f φ = 1 2 c 2 s

16 An overview of brane inflation Combining the ideas studied so far, one can obtain different variation of brane inflation: 1- Single throat slow-roll brane inflation 2- multiple throat slow-roll brane inflation 3- Slow-roll + DBI brane inflation 4- D3-D7 brane inflation in the bulk or in the throat How to embed SM in models of brane inflation? It multiple throats scenario one can consider that in some throat brane inflation takes place while in other throats SM is located. The question of reheating in brane inflation? This seems to be challenging, specially in multi-throat brane inflation.

17 Cosmological Perturbation Theory Now we allow for the perturbations in metric and inflaton field In terms of gauge invariant curvature perturbation the dynamics of perturbation in momentum space is Now the fluctuations propagate with the speed of sound

18 Non-Gaussianities on CMB Simple models of slow-roll inflation predicts almost Gaussian perturbations However, DBI inflation predicts large non-gaussian perturbations k1 What is non-gaussianity? k2 k3 In slow-roll inflation there is not much interaction, Hint ~ 0, so there is no significant non-gaussinities Defining non-gaussianity parameter fnl via ( Simple models of slow roll inflation predict P f NL n s Maldacena, 2002

19 Non-Gaussianities in DBI Inflation The interacting Hamiltonian in DBI inflation is Σ = H2 ɛ c 2 s = Ḣ c 2 s k1 In slow-roll inflation there is no interaction and the level of non-gaussianity is very small. However, for DBI model with a small sound speed, cs << 1, a large non-gaussianity can be obtained. k2 k3 ( f NL 1 c 2 s One can obtain fnl as big as 100, which is easily observed by PLANCK. P This should be compared to slow-roll calculation in which f NL n s Maldacena, 2002

20 The Shapes of Non-Gaussianities Consider the three-point function as so A determines the shapes of the non-gaussianity Shape in DBI inflation Shape in multiple-field models

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23 Alternatives to Inflation: prospects Alternative to inflation includes models of bounce and string gas cosmology. Predictions of bounce scenarios: Produce adiabatic, almost scale invariant perturbations. No appreciable amount of gravitational waves. Significant amount of non-gaussianity. PLANCK may have a good chance to verify or rule out bounce (ekpyrotic)/inflationary scenarios. Open questions and future directions: How to achieve bounce or bypass NEC? Can ekpyrotic models be embedded in high energy physics?

24 Conclusion All observations strongly support inflation as the leading theory of early universe and cosmological structure formation. Simple models of inflation predict almost Gaussian and almost scale invariant perturbations which are in very good agreements with data. Future observations such as PLANCK can put strong constraints on the level of non-gaussianity and may detect the anticipated gravitational waves. Despite its observational successes there is no deep theoretical understanding of inflation dynamics and the nature of the inflaton field. It is an open question if inflation can be embedded in a fundamental theory of high energy physics such as string theory. DBI Inflation is an interesting realization of inflation from high energy physics. It provides a theoretical mechanism to generate large non-gaussianities on CMB which can be detected observationally.