Shortcomings of the inflationary paradigm

Transcription

1 Shortcomings of the inflationary paradigm Looking at the Planck results, Steinhardt et all say:! 1) chaotic inflation with V = O(1) does not work! 2) the only remaining models are the ones with V <<< 1, for which initial conditions for inflation are extremely improbable! Let us show that each of these statements is incorrect! Anna Ijjas, Paul Steinhardt, Avi Loeb Phys. Lett. B 723 (2013), (arxiv: ) & work in progress

2 Why inflation? PHYSICAL REVIEW D VOLUME 23, NUMBER 2 15 JAN UAR Y 1981 Infiationary universe: A possible solution to the horizon and fiatness problems Alan H. Guth* Stanford Linear Accelerator Center, Stanford University, Stanford, California (Received 11 August 1980) The standard model of hot big-bang cosmology requires initial conditions which are problematic in two ways: (1) The early universe is assumed to be highly homogeneous, in spite of the fact that separated regions were causally disconnected (horizon problem); and (2) the initial value of the Hubble constant must be fine tuned to extraordinary accuracy to produce a universe as flat (i.e., near critical mass density) as the one we see today (flatness problem). These problems would disappear if, in its early history, the universe supercooled to temperatures 28 or more orders of magnitude below the critical temperature for some phase transition. A huge expansion factor would then result from a period of exponential growth, and the entropy of the universe would be multiplied by a huge factor when the latent heat is released. Such a scenario is completely natural in the context of grand unified models of elementaryparticle interactions. In such models, the supercooling is also relevant to the problem of monopole suppression. Unfortunately, the scenario seems to lead to some unacceptable consequences, so modifications must be sought. completely described. Now I can explain the puzzles. The first is the 2 well-known horizon problem. The initial unithe standard model of hot big-bang cosmology verse is assumed to be homogeneous, yet it conrelies on the assumption of initial conditions which sists of at least -10" separate regions which are are very puzzling in two ways which I will explain below. The purpose of this paper is to suggest a causally disconnected (i. e., these regions have not yet had time to communicate with each other modified scenario which avoids both of these puzvia light signals). ' (The precise assumptions zles. which lead to these numbers will be spelled out in By "standard model, I refer to an adiabatically Sec. II. ) Thus, one must assume that the forces expanding radiation- dominated universe described Andrei Linde, KITP 23,were 2013 conditions which created initial April these capable by a Robertson-%alker metric. Details will be of violating causality. given in Sec. II. I. INTRODUCTION: THE HORIZON AND FLATNESS PROBLEMS "

3 The idea contracting universe 3 (w + 1) > 3 2 inflationary expanding universe 3 (w + 1) < 1 2 cosmology ekpyrotic/cyclic cosmology

4 conditions for inflation to work (1) inflation occurs, i.e. there is a stage with (2) inflation lasts long enough, i.e. < 1 for 60 >N>0 (3) inflation ends, i.e. > 1 for N =0 (4) inflation gives the right spectrum of density fluctuations, i.e. / 10 5

5 from the equation-of-state to the potential (1) inflation occurs, i.e. there is a stage with = M 2 Pl V 0 2 < 1, = M 2 V 00 Pl < 1 2 V V (2) inflation lasts long enough, i.e. N 1 V M 2 60 Pl V 00 (3) inflation ends, i.e. (1) breaks down for N = 0, (4) inflation gives the right spectrum of density fluctuations, i.e. 1 V 2/3 M 1/3 V Pl

6 classifying inflationary scenarios n s 1=2 6 r = 16 f NL Predictions?

7 Planck2013 in combination with WMAP+SPT+ACT+BAO 1. non-gaussianity is small 2. Planck2013 independently confirms results obtained previously by combining WMAP with other observations. 3. Planck2013 favors a special class of inflationary models: plateau-like potentials

8 Example: new inflation (Albrecht & Steinhardt 1982, Linde 1982) V(φ) V(φ) = λ ( φ 2 - φ 02 ) 2 M I 4 φ 0 ~ M Pl φ Note: energy scale of the plateau is at least 12 orders of magnitude below the Planck scale

9 unlikeliness problem λφ 4 disfavored by Planck2013 less fine-tuning, much larger field-range, larger amount of expansion V(φ) more fine-tuning, much smaller field-range, less amount of expansion λφ λφ 2 a max (power-law) exp(λ -1/2 ) a max (plateau), e a max (plateau) e 100 φ 0 ~ M Pl φ Δφ(plateau) Δφ(power-law) λ -1/4 Δφ(plateau)

10 H Hend N

11 * new initial conditions problem: M I 4 r 3 (t Pl ) > (10 19 GeV / M I ) 3 H -3 (t Pl ) For inflation to start we need huge homogeneous initial volumes Recall that inflation was supposed to explain smoothness, not to assume it! * new multiverse problem: M I 4

12 Quantum creation of the universe! V Creation of the inflationary universe from nothing! Vilenkin 1982,! A.L. 1984,! Vilenkin 1984! σ" Old inflation in string landscape! Hilltop inflation! Fluctuations in the light field σ triggered by old inflation in string theory landscape put this field to the top of the potential in some parts of the universe. After the end of old inflation the new inflation begins.!! Closed ds space cannot continuously grow from the state with a = 0, it must tunnel. For the Planckian H, as in chaotic inflation, the action is O(1), tunneling is easy. For very small H, creation of a closed universe is exponentially suppressed.! No problem with initial conditions!! Cornish, Starkman, Spergel 1996; A.L Like in hybrid inflation, but with symmetry breaking σ >> 1 Inflation begins naturally, as in large field chaotic inflation! Hybrid! Hilltop! -10! 10! 20!! The size of a torus (our universe) with relativistic matter grows as t1/2, whereas the mean free path of a relativistic particle grows much faster, as t! Therefore until the beginning of inflation the universe remains smaller that the size of the horizon ~ t!

13 Future data will... (a) diffuse the problems, (b) confirm the problems, or (c) amplify the problems. Thank you!