Breaking the symmetry

Transcription

1 Breaking the symmetry accelerated expansion without dark energy Syksy Räsänen University of Helsinki Department of Physics and The Helsinki Institute of Physics 1

2 Physics Nobel prize 2011 for the discovery of the accelerating expansion of the Universe through observations of distant supernovae Saul Perlmutter Brian P. Schmidt Adam G. Riess 2

3 3

4 Isotropy 4

5 Homogeneity University of Pavia colloquim,

6 The Friedmann-Robertson- Walker model The universe is usually taken to be exactly homogeneous and isotropic. Such a model with normal matter and normal gravity works for the early universe. However, it underpredicts distances and expansion rates at late times by a factor of 2. 6

7 A factor of 2 Three alternatives: 1) There is matter with negative pressure. 2) General relativity does not hold. 3) The homogeneous and isotropic approximation is not valid. 7

8 Dark energy The most popular alternative is dark energy. Dark energy is a form of matter that has negative pressure, does not absorb or emit light and is evenly spread in the universe. Best candidate is vacuum energy, also known as the cosmological constant. Fits observations well. dark energy [...] is an enigma, perhaps the greatest in physics today 8

9 Transition to acceleration Vacuum energy modifies the expansion rate at late times: 3!a2 a 2 3H 2 = 8πG N (ρ r0 a 4 + ρ m0 a 3 + ρ Λ0 ). 5.0 Ht loghtêyrl t eq << t << t Λ a(t) t 2/3 Ht = 2 / 3 t >> t Λ a(t) e 8πG Nρ /3t Λ 0 Ht 9 t

10 Transition to acceleration Vacuum energy modifies the expansion rate at late times: 3!a2 a 2 3H 2 = 8πG N (ρ r0 a 4 + ρ m0 a 3 + ρ Λ0 ) Ht têgyr loghtêyrl t eq << t << t Λ a(t) t 2/3 Ht = 2 / 3 t >> t Λ a(t) e 8πG Nρ /3t Λ 0 Ht 10 t

11 The coincidence problem As the universe expands, the energy density of normal matter drops inversely to the volume. Vacuum energy density stays constant. How come we are living in the era when vacuum energy has just become important? What s special about 10 billion years? 11

12 Structure formation University of Pavia colloquim,

13 The backreaction conjecture At late times, the universe is only statistically homogeneous and isotropic, on scales >100 Mpc. The average evolution of a clumpy spacetime is not the same as the evolution of a smooth spacetime, a feature known as backreaction. (Ellis: 1984, Buchert, Räsänen: ) The relation between expansion rate and light propagation can also change. (Räsänen: ) The average expansion rate of a clumpy spacetime can accelerate, even though the expansion decelerates locally. 13

14 Understanding acceleration The average expansion rate can increase, because the fraction of volume in faster regions grows. Structure formation involves overdense regions decelerating more and underdense regions decelerating less. Acceleration can be demonstrated with a toy model which has one overdense and one underdense region. (Räsänen: astro-ph/ ) H a 3 a = a 1 a a H a 2 3 a a 2 3 H 2 = v 1 H 1 + v 2 H 2 a a = v 1 a 1 + v 2 a 1 a 2 a 2 + 2v 1 v 2 (H 1 H 2 ) 2 14

15 A simple estimate Take a smooth background with an initial Gaussian linear density field. Identify structures with spherical isolated peaks of the smoothed density field. (Räsänen: ) Each peak evolves separately. The peak number density as a function of time is determined by the power spectrum. The expansion rate is H(t) = 1 dδ v δ (t)h δ (t). 15

16 Two things right The peak model gets the amplitude and the timing right. 2/3 < Ht < 1 because the volume is dominated by underdense voids. 16

17 The timestamp of 10 billion years 3!a2 a 2 3H 2 = 8πG N (ρ r0 a 4 + ρ m0 a 3 ) t << t eq a(t) t 1/2 Ht =1/ 2 t eq << t a(t) t 2/3 Ht = 2 / 3 The amplitude of small wavelength perturbations is suppressed. Structure formation proceeds from small to large scales, so the number density of peaks rises with time. The timescale t A -3/2 t eq yr is imprinted on the perturbation spectrum, where A=3x10-5 is the amplitude of initial perturbations. 17

18 Towards reality beyond Newton Acceleration due to structures is possible: is it realised in the universe? Non-linear evolution is studied with N-body simulations. Simulations use Newtonian gravity with periodic boundary conditions. In Newtonian gravity, backreaction reduces to a boundary term. (Buchert, Ehlers: astro-ph/ ) This is not true in general relativity. (Buchert: gr-qc/ ) 18

19 So how about the details? In 2010, a new formalism for perturbations was introduced, with the claim that it shows that backreaction is small. (Green, Wald: ) However, there are issues. (Buchert et al: ) The formalism assumes that perturbations are small, from which the conclusion follows without the new formalism. (Räsänen: ) 19

20 Open questions Is the universe close to FRW? If not, should see breakdown of perturbation theory. If non-newtonian effects are important, how to model them? Recent development: fully non-linear relativistic cosmological simulations. (Bentivegna, Bruni: , Giblin, Mertens, Starkman: , ) More quantitatively relating the average expansion rate and light propagation. 20

21 Absence of observational evidence Vacuum energy for acceleration was proposed in the 1980 s, and became prominent in Since then, there has been no evidence for deviation from vacuum energy concordance model. The posterior probability of any explanation that did not predict only small deviations from vacuum energy is therefore smaller. This does not mean that evolution quite different from the vacuum energy case is disallowed. 21

22 Signatures of backreaction If backreaction is significant, the universe is not on average described by the FRW metric. Backreaction is tested by consistency conditions of the FRW metric. (Clarkson, Bassett, Lu: ) d(z) = 1 k sinh # k z dz' & % ( k 0 H = 1 h(z)2 d '(z) 2 $ h(z') ' d(z) 2 Also measurements of cosmic parallax and the distance sum rule. (Räsänen: , ) 22

23 The road ahead Observations are inconsistent with homogeneous and isotropic models with normal matter and gravity. Vacuum energy fits observations, but makes people uneasy. Structure formation has a timescale of 10 billion years. If the metric is close to FRW, backreaction is small. If non-newtonian effects can be neglected, backreaction is small. More work is necessary to quantify the effect before concluding that new fundemental physics is needed. 23