Atick-Witten Hagedorn conjecture, near scale-invariant matter and blue-tilted gravity power spectrum

Abstract

We will provide an interesting new mechanism to generate almost scale invariant seed density perturbations with a red spectrum, while keeping the gravitational wave spectrum blue-tilted in a stringy thermal contracting phase at temperatures beyond the Hagedorn temperature. This phase is often referred to as the Hagedorn phase where the free energy has been conjectured by Atick and Witten to grow more slowly than ordinary radiation. The primordial fluctuations are created by the statistical thermal fluctuations determined by the partition function, rather than quantum vacuum driven fluid dynamical fluctuations. Our mechanism assumes a non-singular bounce.

String-inspired infinite-derivative theories of gravity: A brief overview

“…Bounce inflation [28][29][30] has become a particularly interesting cosmological scenario for several reasons: It provides a nonsingular geodesic completeness to inflationary space-time; it is naturally suited to address the low multipole anomalies 28 in CMB as the near exponential inflation is necessarily preceded by a super inflationary phase; it also provides a way of stretching matter and gravity wave fluctuations that may be produced during the contracting phase to cosmological scales during subsequent inflation thereby making them relevant for CMB. 30 Since our IDG models can provide such Bounce inflationary solutions, it becomes interesting to investigate the viability of these models further by looking into the fluctuations around the backgrounds. Such an investigation has proved to be rather challenging and technical but progress have been made.…”

Numerically investigating the emergent cyclic inflation scenario

“…Imprints of thermal fluctuations was calculated in [34]. In [27] another rather interesting possibility of producing a relatively large tensor-to-scalar ratio and a blue gravity wave tilt was proposed that can easily be applied to the CI scenario. This would however require extending the model investigated in this paper with stringy Hagedorn phases [64].…”

Blue tensor spectrum from particle production during inflation

“…A solution to this possible tension may be a blue tilt in the tensor spectrum [25], which would then result in a running of the tensor-to-scalar-ratio, T r ≡ d ln r d ln k = n T − (n s − 1) [26], where n s and n T are the scalar and tensor spectral indices, respectively. While standard single-field slow-roll inflation satisfies n T = −r/8, a significant blue tensor tilt can be attained -besides from the particle production mechanism that we study here -with generalized slow-roll [27], non-Bunch Davies initial states [28] (extending [29]), sourcing from a spectator field with small sound speed [30], other non-standard inflationary scenarios [31][32][33], and some noninflationary mechanisms [34]. Other ideas to reconcile this possible tension include invoking a negative running of the scalar spectral index [1,[35][36][37][38][39][40][41], suppression of the scalar power at large scales [42][43][44][45][46][47], anti-correlated isocurvature perturbations [48][49][50], a space-dependent r [51], cosmological birefringence [52], dark radiation [53][54][55], primordial magnetic fields [56], a pre-inflationary bounce [57], and sterile neutrinos [58][59][60][61][62].…”