Primordial GW from pseudoscalar inflation.

Transcription

1 Primordial GW from pseudoscalar inflation. Mauro Pieroni Laboratoire APC, Paris. July 6, 2016

2 Overview 1 A review on inflation. 2 GW from a Pseudoscalar inflaton. 3 Conclusions and future perspectives.

3 Standard single field slow roll inflation. Homogeneus scalar field φ in a homogeneous and isotropic universe: S = d 4 x ( R g 2κ + φ ) V (φ), ds 2 = dt 2 + a 2 (t)d x 2 (1) Friedmann + e.o.m. for φ fix the evolution (κ 2 = 1): ( ) 2 ȧ H 2 = ρ a 3, 2Ḣ = p + ρ V φ + 3H φ + φ = 0. (2) Inflation Early phase of exponential expansion ( ) 2 ds Spacetime H 2 ȧ = const Eternally inflating universe a ( ) 2 ȧ const ρ p const φ 2 a 2 V const Nearly ds space Inflation Good inflationary models Slow departure from 1 + p/ρ 0.

4 Direct GW detection. Inflation predicts a nearly scale invariant scalar and tensor power spectra. The produced signal is outside of the sensitivity curves both of present and future direct GW detectors.

5 Overview 1 A review on inflation. 2 GW from a Pseudoscalar inflaton. 3 Conclusions and future perspectives.

6 Pseudoscalar inflation in presence of Gauge fields. Pseudoscalar inflaton with a non-minimal coupling with some gauge fields: L = M2 p 2 R 1 2 µφ µ φ V (φ) 1 4 FµνF µν α 4Λ φfµν F µν (3) d 2 A a (τ, k) dτ 2 The equations of motion for the fields are: φ + 3H φ + V φ = α Λ E B (4) 2 A a α dφ Λ dτ A a = 0 (5) Friedmann equation reads: dt a dτ 3H 2 = 1 2 φ 2 + V (φ)+ 1 2 E 2 + B 2. (6) The equations of motion for the gauge fields in Fourier transform are: d 2 A a (τ, k) dτ 2 k 2 A a + i α Λ dφ dτ k A a = 0 (7)

7 Gauge field amplification. Taking k parallel to ˆx, we use the helicity vectors e ± = (ŷ ± iẑ)/ 2 to get: A a = e ±A a ± k A a = A a ± k e ± = ia a ± k e ± (8) The equations of motion for the Fourier transform of the gauge fields read: d 2 A a ±(τ, [ k) + k 2 ±2k ξ ] A a ±(τ, dτ 2 τ k) = 0, ξ α φ 2HΛ ɛ H. (9) If ξ is nearly constant the gauge fields are exponentially growing with ξ. As E B ( ) H N ξ e 2πξ, and the equation of motion for φ is: φ + 3H φ + V φ = α Λ E B. (10) The friction term induced by the gauge fields is exponentially growing with ξ. This term dominates the last part of the evolution. Modified dynamics also affects the scalar and tensor power spectra!

8 Modified scalar spectrum. ( ) H 2 2 ( α E Scalar spectrum P s(k) = 2π φ + B ) 2 3bH φ (11) where: COBE normalization fixes V 0 Stong increase at small scales PBHs Nearly universal behavior at large scales 1 N (2πξ) 2 P s(k) at small scales b 1 2πξ α E B 3ΛH phi (12) ɛ H O(1) N p V. Domcke, M.P. and P. Binétruy, arxiv: [astro-ph.co].

9 V. Domcke, M.P. and P. Binétruy, arxiv: [astro-ph.co]. Modified tensor spectrum. GW spectrum P t(k) = 1 ( ) 2 ) H ( H 2 12 πm p Mp 2 ξ 6 e4πξ N-frequency relation N = N CMB + ln (14) k CMB Mpc 44.9 ln f Hz. (15) Spectra asymptote to an universal value at small scales Low scale models (p = 3, 4) have a stronger increase Some models produce GW in the observable range of direct GW detectors ɛ H O(1) N p

10 Starobinsky-like model parameter space. Models with p = 2 give a potential : V (φ) V 0 (1 exp{ γφ}) 2 V. Domcke, M.P. and P. Binétruy, arxiv: [astro-ph.co]. The complementarity between different measures can be used to restrict the parameter space!

11 Overview 1 A review on inflation. 2 GW from a Pseudoscalar inflaton. 3 Conclusions and future perspectives.

12 Conclusions and future perspectives. Main results: Possible generation of Primoridal GWs in the observable ranges for direct GW detectors. If this GW are observed, we get important informations on the microphysics of inflation. Models with large n s may be recovered. Future perspectives: More models. Extension to Non-abelian gauge fields. Consequences on reheating. Generation of PBH. Embedding in a UV complete theory.

13 The End Thank you

14

15