Fluctuations in Non-Singular Bouncing Motivation Cosmologies from - PowerPoint PPT Presentation

String Bounce R. Branden- berger Fluctuations in Non-Singular Bouncing Motivation Cosmologies from Type II Superstrings Alternatives Perturbations Superstring Bounce Robert Brandenberger S-Brane McGill University Fluctuations Conclusions March 16, 2012 Work in collaboration with C. Kounnas, H. Partouche, S. Patil and N. Toumbas arXiv/1203xxxx 1 / 51

Outline String Bounce R. Branden- berger Motivation 1 Motivation Alternatives Alternatives 2 Perturbations Superstring Cosmological Perturbations 3 Bounce S-Brane Fluctuations Bouncing Type II Superstring Cosmology 4 Conclusions Fluctuations in Bouncing Type II Superstring Cosmology 5 6 Conclusions 2 / 51

Plan String Bounce R. Branden- berger Motivation 1 Motivation Alternatives Alternatives 2 Perturbations Superstring Cosmological Perturbations 3 Bounce S-Brane Fluctuations Bouncing Type II Superstring Cosmology 4 Conclusions Fluctuations in Bouncing Type II Superstring Cosmology 5 6 Conclusions 3 / 51

Space-time sketch of inflationary cosmology String Bounce The Inflationary Universe Scenario is the current paradigm R. Branden- of early universe cosmology. berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions Note: H = ˙ a a curve labelled by k : wavelength of a fluctuation 4 / 51

Space-time sketch of inflationary cosmology String Bounce The Inflationary Universe Scenario is the current paradigm R. Branden- of early universe cosmology. berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions Note: H = ˙ a a curve labelled by k : wavelength of a fluctuation 4 / 51

Successes of Inflation String Bounce R. Branden- berger Motivation inflation renders the universe large, homogeneous and Alternatives spatially flat Perturbations Superstring classical matter redshifts → matter vacuum remains Bounce S-Brane quantum vacuum fluctuations: seeds for the observed Fluctuations structure [Chibisov & Mukhanov, 1981] Conclusions sub-Hubble → locally causal 5 / 51

String Bounce R. Branden- berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions Credit: NASA/WMAP Science Team 6 / 51

String Bounce R. Branden- berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions Credit: NASA/WMAP Science Team 7 / 51

Trans-Planckian Problem for Fluctuations String Bounce R. Branden- berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions Success of inflation : At early times scales are inside the Hubble radius → causal generation mechanism is possible. Problem: If time period of inflation is more than 70 H − 1 , then λ p ( t ) < l pl at the beginning of inflation → new physics MUST enter into the calculation of the fluctuations. 8 / 51

Trans-Planckian Problem for Fluctuations String Bounce R. Branden- berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions Success of inflation : At early times scales are inside the Hubble radius → causal generation mechanism is possible. Problem: If time period of inflation is more than 70 H − 1 , then λ p ( t ) < l pl at the beginning of inflation → new physics MUST enter into the calculation of the fluctuations. 8 / 51

Trans-Planckian Problem for Fluctuations String Bounce R. Branden- berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions Success of inflation : At early times scales are inside the Hubble radius → causal generation mechanism is possible. Problem: If time period of inflation is more than 70 H − 1 , then λ p ( t ) < l pl at the beginning of inflation → new physics MUST enter into the calculation of the fluctuations. 8 / 51

String Bounce R. Branden- berger Recent Reference: A. Linde, V. Mukhanov and A. Vikman, arXiv:0912.0944 Motivation Alternatives It is not sufficient to show that the Hubble constant is Perturbations smaller than the Planck scale. Superstring Bounce The frequencies involved in the analysis of the S-Brane cosmological fluctuations are many orders of Fluctuations magnitude larger than the Planck mass. Thus, “the Conclusions methods used in [1] are inapplicable for the description of the .. process of generation of perturbations in this scenario." 9 / 51

Applicability of GR String Bounce R. Branden- berger In all approaches to quantum gravity, the Einstein action Motivation is only the leading term in a low curvature expansion. Alternatives Correction terms may become dominant at much lower Perturbations energies than the Planck scale. Superstring Bounce Correction terms will dominate the dynamics at high S-Brane curvatures. Fluctuations Conclusions The energy scale of inflation models is typically η ∼ 10 16 GeV. → η too close to m pl to trust predictions made using GR. 10 / 51

Cosmological Constant Problem String Bounce R. Branden- berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Quantum vacuum energy does not gravitate. Fluctuations Conclusions Why should the almost constant V ( ϕ ) gravitate? V 0 ∼ 10 120 Λ obs 11 / 51

Zones of Ignorance String Bounce R. Branden- berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions 12 / 51

Message String Bounce R. Branden- berger Current realizations of inflation have serious conceptual Motivation problems. Alternatives This motivates the search for alternatives. Perturbations Superstring Key principles of string theory lead to alternatives to Bounce cosmological inflation. S-Brane Fluctuations Alternative A: String Gas Cosmology Conclusions Alternative B: Matter Bounce. Topic of this lecture! Specific predictions allow the models to be distinguished from inflationary cosmology. 13 / 51

Message String Bounce R. Branden- berger Current realizations of inflation have serious conceptual Motivation problems. Alternatives This motivates the search for alternatives. Perturbations Superstring Key principles of string theory lead to alternatives to Bounce cosmological inflation. S-Brane Fluctuations Alternative A: String Gas Cosmology Conclusions Alternative B: Matter Bounce. Topic of this lecture! Specific predictions allow the models to be distinguished from inflationary cosmology. 13 / 51

Message String Bounce R. Branden- berger Current realizations of inflation have serious conceptual Motivation problems. Alternatives This motivates the search for alternatives. Perturbations Superstring Key principles of string theory lead to alternatives to Bounce cosmological inflation. S-Brane Fluctuations Alternative A: String Gas Cosmology Conclusions Alternative B: Matter Bounce. Topic of this lecture! Specific predictions allow the models to be distinguished from inflationary cosmology. 13 / 51

Message String Bounce R. Branden- berger Current realizations of inflation have serious conceptual Motivation problems. Alternatives This motivates the search for alternatives. Perturbations Superstring Key principles of string theory lead to alternatives to Bounce cosmological inflation. S-Brane Fluctuations Alternative A: String Gas Cosmology Conclusions Alternative B: Matter Bounce. Topic of this lecture! Specific predictions allow the models to be distinguished from inflationary cosmology. 13 / 51

Message String Bounce R. Branden- berger Current realizations of inflation have serious conceptual Motivation problems. Alternatives This motivates the search for alternatives. Perturbations Superstring Key principles of string theory lead to alternatives to Bounce cosmological inflation. S-Brane Fluctuations Alternative A: String Gas Cosmology Conclusions Alternative B: Matter Bounce. Topic of this lecture! Specific predictions allow the models to be distinguished from inflationary cosmology. 13 / 51

Message String Bounce R. Branden- berger Current realizations of inflation have serious conceptual Motivation problems. Alternatives This motivates the search for alternatives. Perturbations Superstring Key principles of string theory lead to alternatives to Bounce cosmological inflation. S-Brane Fluctuations Alternative A: String Gas Cosmology Conclusions Alternative B: Matter Bounce. Topic of this lecture! Specific predictions allow the models to be distinguished from inflationary cosmology. 13 / 51

Plan String Bounce R. Branden- berger Motivation 1 Motivation Alternatives Alternatives 2 Perturbations Superstring Cosmological Perturbations 3 Bounce S-Brane Fluctuations Bouncing Type II Superstring Cosmology 4 Conclusions Fluctuations in Bouncing Type II Superstring Cosmology 5 6 Conclusions 14 / 51

Space-Time Sketch of Inflationary Cosmology String Bounce R. Branden- berger Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions N.B. Perturbations originate as quantum vacuum fluctuations. 15 / 51

Emergent Universe Scenario String Bounce R. Branden- berger Background dynamics for the scale factor a ( t ) : Motivation Alternatives Perturbations Superstring Bounce S-Brane Fluctuations Conclusions 16 / 51