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تسجيل مستخدم جديدStochastic emergence of inflaton fluctuations in a SdS primordial universe with large-scale repulsive gravity from a 5D vacuum
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We develop a stochastic approach to study scalar field fluctuations of the inflaton field in an early inflationary universe with a black-hole (BH), which is described by an effective 4D SdS metric. Considering a 5D Ricci-flat SdS static metric, we implement a planar coordinate transformation, in order to obtain a 5D cosmological metric, from which the effective 4D SdS metric can be induced on a 4D hypersurface. We found that at the end of inflation, the squared fluctuations of the inflaton field are not exactly scale independent and becomes sensitive with the mass of the BH.
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We develop a non-perturbative formalism for scalar metric fluctuations from a 5D extended version of general relativity in vacuum. In this work we concentrate our efforts on calculations valid on large cosmological scales, which are the dominant duri
ng the inflationary phase of the universe. The resulting metric in this limit is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution. We calculate the spectrum of these fluctuations with an effective 4D Schwarzschild-de Sitter spacetime on cosmological scales, which is obtained after we make a static foliation on the non-compact extra coordinate. Our results show how the squared metric fluctuations of the primordial universe become scale invariant with the inflationary expansion.
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Luz Marina Reyes
, Claudia Moreno
, Jose Edgar Madriz Aguilarn (Departamento de Matematicas
2012
We investigate, in the transverse traceless (TT) gauge, the generation of the relic background of gravitational waves, generated during an early inflationary stage, on the framework of a large-scale repulsive gravity model. We calculate the spectrum
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Scalar perturbations during inflation can be substantially amplified by tiny features in the inflaton potential. A bump-like feature behaves like a local speed-breaker and lowers the speed of the scalar field, thereby locally enhancing the scalar pow
er spectrum. A bump-like feature emerges naturally if the base inflaton potential $V_b(phi)$ contains a local correction term such as $V_b(phi)left[1+varepsilon(phi)right]$ at $phi=phi_0$. The presence of such a localised correction term at $phi_0$ leads to a large peak in the curvature power spectrum and to an enhanced probability of black hole formation. Remarkably this does not significantly affect the scalar spectral index $n_{_S}$ and tensor to scalar ratio $r$ on CMB scales. Consequently such models can produce higher mass primordial black holes ($M_{rm PBH}geq 1 M_{odot}$) in contrast to models with `near inflection-point potentials in which generating higher mass black holes severely affects $n_{_S}$ and $r$. With a suitable choice of the base potential - such as the string theory based (KKLT) inflation or the $alpha$-attractor models - the amplification of primordial scalar power spectrum can be as large as $10^7$ which leads to a significant contribution of primordial black holes (PBHs) to the dark matter density today, $f_{rm PBH} = Omega_{0,rm PBH}/Omega_{0,rm DM} sim O(1)$. Interestingly, our results remain valid if the bump is replaced by a dip. In this case the base inflaton potential $V_b(phi)$ contains a negative local correction term such as $V_b(phi)left[1-varepsilon(phi)right]$ at $phi=phi_0$ which leads to an enhanced probability of PBH formation. We conclude that primordial black holes in the mass range $10^{-17} M_{odot} leq M_{rm PBH} leq 100, M_{odot}$ can easily form in single field inflation in the presence of small bump-like and dip-like features in the inflaton potential.
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