Gravitational waves and large field inflation

According to the famous Lyth bound, one can confirm large field inflation by finding tensor modes with sufficiently large tensor-to-scalar ratio $r$. Here we will try to answer two related questions: Is it possible to rule out all large field inflationary models by not finding tensor modes with $r$ above some critical value, and what can we say about the scale of inflation by measuring $r$? However, in order to answer these questions one should distinguish between two different definitions of the large field inflation and three different definitions of the scale of inflation. We will examine these issues using the theory of cosmological $\alpha$-attractors as a convenient testing ground.

[1]  Alexei A. Starobinsky.  The Perturbation Spectrum Evolving from a Nonsingular Initially De-Sitter Cosmology and the Microwave Background Anisotropy , 1983 .

[2]  A. B. Goncharov,et al.  Chaotic inflation in supergravity , 1984 .

[3]  Andrei Linde,et al.  Universal attractor for inflation at strong coupling. , 2013, Physical review letters.

[4]  M. Zaldarriaga,et al.  Implications of the scalar tilt for the tensor-to-scalar ratio , 2014, 1412.0678.

[5]  David H. Lyth,et al.  What Would We Learn by Detecting a Gravitational Wave Signal in the Cosmic Microwave Background Anisotropy , 1997 .

[6]  Adrian T. Lee,et al.  CMB-S4 Science Book, First Edition , 2016, 1610.02743.

[7]  Andrew R. Liddle,et al.  The Primordial Density Perturbation: Cosmology, Inflation and the Origin of Structure , 2009 .

[8]  A. Starobinsky,et al.  A new type of isotropic cosmological models without singularity , 1980 .

[9]  R. W. Ogburn,et al.  Improved Constraints on Cosmology and Foregrounds from BICEP2 and Keck Array Cosmic Microwave Background Data with Inclusion of 95 GHz Band. , 2016, Physical review letters.

[10]  Andrei Linde.  Initial conditions for inflation , 1985 .

[11]  Viatcheslav Mukhanov,et al.  Quantum Fluctuations and a Nonsingular Universe , 1981 .

[12]  Andrei Linde,et al.  Superconformal inflationary α-attractors , 2013, 1311.0472.

[13]  G. W. Pratt,et al.  Planck 2015. XX. Constraints on inflation , 2015, 1502.02114.

[14]  S. Ferrara,et al.  Seven-Disk Manifold, α-attractors and B-modes , 2016 .

[15]  Andrei Linde,et al.  Escher in the Sky , 2015, Comptes Rendus Physique.

[16]  R. Flauger,et al.  Robustness of inflation to inhomogeneous initial conditions , 2016, 1608.04408.

[17]  Andrei Linde,et al.  Universality class in conformal inflation , 2013, 1306.5220.

[18]  C. A. Oxborrow,et al.  Planck2015 results , 2015, Astronomy & Astrophysics.

[19]  Andrei Linde,et al.  Hyperbolic geometry of cosmological attractors , 2015, 1504.05557.

[20]  L. Senatore,et al.  Beginning inflation in an inhomogeneous universe , 2015, Journal of Cosmology and Astroparticle Physics.

[21]  Kazuhiro Yamamoto,et al.  Constraints on α -attractor inflation and reheating , 2016, 1602.07427.

[22]  V. Mukhanov.  Quantum cosmological perturbations: predictions and observations , 2013, 1303.3925.

[23]  A. A. Starobinskii.  The perturbation spectrum evolving from a nonsingular, initially de Sitter cosmology, and the microwave background anisotropy , 1983 .

[24]  Andrei Linde,et al.  Particle Physics and Inflationary Cosmology , 1988 .

[25]  Andrei Linde,et al.  Cosmological attractors and initial conditions for inflation , 2015, Physical Review D.

[26]  L. Senatore,et al.  Inhomogeneous anisotropic cosmology , 2016, 1602.03520.

[27]  M. Shaposhnikov,et al.  The Standard Model Higgs boson as the inflaton , 2007, 0710.3755.

[28]  G. W. Pratt,et al.  Planck 2013 results. XXII. Constraints on inflation , 2013, 1303.5082.

[29]  D. Roest.  Universality classes of inflation , 2013, 1309.1285.

[30]  Andrei Linde,et al.  Unity of cosmological inflation attractors. , 2015, Physical review letters.

[31]  Andrei Linde,et al.  Minimal Supergravity Models of Inflation , 2013, 1307.7696.

[32]  Andrei Linde,et al.  Cosmological attractors and asymptotic freedom of the inflaton field , 2016, 1604.00444.

[33]  Andrei Linde,et al.  CHAOTIC INFLATION OF THE UNIVERSE IN SUPERGRAVITY , 1985 .

[34]  Jérôme Martin,et al.  Shortcomings of New Parametrizations of Inflation , 2016, 1609.04739.

[35]  J. Bond,et al.  Designing density fluctuation spectra in inflation. , 1989, Physical review. D, Particles and fields.

[36]  Andrei Linde.  Does the first chaotic inflation model in supergravity provide the best fit to the Planck data? , 2014, 1412.7111.

[37]  S. Ferrara,et al.  Seven-Disk Manifold, alpha-attractors and B-modes , 2016, 1610.04163.

[38]  Andrei Linde,et al.  Superconformal generalization of the chaotic inflation model , 2013, 1306.3211.

[39]  J. García-Bellido,et al.  Lyth bound of inflation with a tilt , 2014, 1408.6839.