Shortcomings of the inflationary paradigm Anna Ijjas, Paul - PowerPoint PPT Presentation

Shortcomings of the inflationary paradigm Anna Ijjas, Paul Steinhardt, Avi Loeb Phys. Lett. B 723 (2013), 261-266 (arXiv: 1304.2785) & work in progress

Why inflation? 15 JAN UAR Y 1981 VOLUME 23, NUMBER PHYSICAL REVIEW 2 D universe: A possible solution to the horizon and fiatness problems Infiationary Alan H. Guth* Stanford Linear Accelerator Center, Stanford California 94305 Stanford, University, (Received 11 August 1980) The standard model of hot big-bang cosmology requires initial conditions which are problematic in two ways: (1) in spite of the fact that separated The early universe is assumed to be highly regions were causally homogeneous, (horizon problem); and (2) the initial value of the Hubble constant must be fine tuned to extraordinary disconnected accuracy to produce a universe as flat (i. e. , near critical mass density) as the one we see today (flatness problem). to temperatures 28 or more orders These problems would disappear if, in its early history, the universe supercooled of magnitude below the critical temperature for some phase transition. A huge expansion factor would then result from a period of exponential and the entropy of the universe would be multiplied by a huge factor when the growth, in the context of grand models of elementary- latent heat is released. Such a scenario is completely natural unified In such models, to the problem of monopole particle interactions. the supercooling is also relevant suppression. the scenario seems to lead to some unacceptable so modifications must be sought. Unfortunately, consequences, described. I. INTRODUCTION: completely THE HORIZON AND FLATNESS Now I can explain The first is the PROBLEMS the puzzles. well-known horizon problem. 2 The initial uni- The standard model of hot big-bang cosmology verse is assumed relies on the assumption yet it con- of initial conditions to be homogeneous, which sists of at least -10" separate are very puzzling in two ways which I will explain which are regions (i. e. , these regions of this paper is to suggest a below. The purpose causally disconnected have scenario which avoids both of these puz- with each other modified not yet had time to communicate via light signals). ' zles. (The precise assumptions model, " I refer to an adiabatically By "standard which lead to these numbers will be spelled out in Sec. II. ) Thus, that the forces radiation- dominated universe described one must assume expanding Andrei Linde, KITP April 23, 2013 by a Robertson-%alker metric. Details will be which created these initial conditions were capable given in Sec. II. of violating causality. I would first like Before explaining The second puzzle is the flatness the puzzles, problem. This my notion of "initial conditions. " The to clarify puzzle seems to be much less celebrated than the which is conven- first, but it has been stressed by Dicke and Pee- standard model has a singularity taken to be at time t =0. As t -0, the bles. I feel that it is of comparable importance tionally T — ~. to the first. It is known temperature no initial-value prob- that the energy density Thus, p today is near the critical value p„ lem can be defined at t=0. when T is of the universe However, (Mz, —= I/~6=1. 22 to the borderline of the order of the Planck mass (corresponding between an open &&10~~ GeV)' or greater, and closed universe). One can safely assume of the stan- that~ the equations 0. 01 & Q& ( 10, dard model are undoubtedly since meaningless, to be- effects are expected gravitational quantum where come essential. the scope of our Thus, within knowl, edge, it is sensible to begin the hot big-bang 0 — = p/p„= (8w/3)Gp/H2, To which is com- scenario at some temperature below Mp, let us say To — 10" GeV. — and the subscript the value at the present p denotes fortably At do not appear at first time. these bounds this time one can take the description of the uni- Although in fact, verse as a set of initial conditions, sight to be remarkably stringent, they, and the equa- The key point is that then describe have powerful implications. tions of motion evolu- the subsequent the condition 0=1 is unstable. Furthermore, Of course, of state for matter the tion. the equation for is not really only time scale which appears at these temperatures in the equations but one known, universe is the Planck time, can make various the con- a radiation-dominated hypotheses and pursue 1/I„= 5. 4 && 10 sec. A typical closed universe sequences. the initial universe is will reach its maximum size on the order of this In the standard model, and isotropic, time scale, while a typical and filled open universe will taken to be homogeneous to a value of p much less than p„. A uni- with a gas of effectively massless particles in dwindle verse can survive -10' years only The ini- by extreme fine thermal at temperature equilibrium To. of p and H, so that p is "constant" H is tial value of the Hubble of the initial values expansion tuning very near p„. For the initial is then taken to be Ho, and the model universe conditions taken at

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

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. δρ / ρ ∼ 10 − 5

from the equation-of-state to the potential (1) inflation occurs, i.e. there is a stage with ◆ 2 � � V 00 ✏ = M 2 ✓ V 0 | η | = M 2 � � Pl � < 1 < 1 , � � Pl V 2 V � (2) inflation lasts “long enough”, i.e. V 1 N ∼ V 00 ∼ 60 M 2 Pl (3) inflation ends, i.e. (1) breaks down for N = 0, (4) inflation gives the right spectrum of density fluctuations, i.e. V 2 / 3 δρ 1 ∼ 10 � 5 ρ ∼ M 1 / 3 V 0 Pl

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

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

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

“unlikeliness problem” disfavored by Planck2013 less fine-tuning, much larger field-range, ∼ 𝜇𝜚 4 larger amount of expansion a max ( power-law ) V( 𝜚 ) ¡ ∼ exp( 𝜇 -1/2 ) a max ( plateau ) , ∼ e 10000000000 more fine-tuning, much smaller field-range, less amount of expansion ∼ 𝜇𝜚 0 4 - 𝜇𝜚 2 a max ( plateau ) ∼ e 100 ¡ 𝜚 ¡ 𝜚 0 ~ M Pl ¡ 𝛦𝜚 ( plateau ) 𝛦𝜚 ( power-law ) ∼ 𝜇 -1/4 𝛦𝜚 ( plateau )

H Hend 60 50 40 30 20 10 N 10 20 30 40 50 60

* new initial conditions problem: 4 ¡ M I 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: 4 ¡ M I

Quantum creation of the universe ! V Creation of the inflationary universe from nothing ! Vilenkin 1982, ! A.L. 1984, ! σ" Vilenkin 1984 ! “Old inflation” in string landscape ! Hilltop inflation ! Fluctuations in the light field σ triggered by “old inflation” in string theory landscape Closed dS space cannot continuously grow from the state put this field to the top of the potential in some parts of the universe. After the end of with a = 0, it must tunnel. For the Planckian H, as in chaotic “old inflation” the new inflation begins. ! ! inflation, the action is O(1), tunneling is easy. For very small H, No problem with initial conditions! ! creation of a closed universe is exponentially suppressed . ! Cornish, Starkman, Spergel 1996; A.L. 2004 The size of a torus (our universe) with relativistic matter grows as Like in hybrid inflation, but with symmetry breaking σ >> 1 ! t 1/2 , whereas the mean free path of Inflation begins naturally, as in large field chaotic inflation ! a relativistic particle grows much faster, as t ! Hybrid ! Hilltop ! Therefore until the beginning of inflation the universe remains -10 ! smaller that the size of σ σ the horizon ~ t ! 10 ! 20 !

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