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Register a new userThe Quantum Origin of Quasi de Sitter: a Model Independent Quantum Cosmological Tilt
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The most robust prediction of inflationary cosmology is the existence of a red tilt for the spectrum of curvature fluctuations that is experimentally of order $0.04$. The tilt is derived solving the exact equation for quantum fluctuations in a quasi de Sitter background defined by a equation of state $epsilon equiv frac{(p+rho)}{rho}$ with $epsilon$ small but non vanishing. The experimental data selects among the different quasi de Sitter inflaton potentials. The origin of the lack of scale invariance associated with the tilt is however classical in essence and parametrized by the slow roll of the inflaton potential. Here we present a purely quantum mechanical and model independent derivation of the tilt. This derivation is based on two basic observations: first, the correlator for gauge invariant variables is related to the {it quantum Fisher function} measuring the quantum dependence of the family of pure de Sitter vacua on the energy scale parameter; second, this quantum Fisher function has a non vanishing scale dependent red tilt that, at the energy scales of physical interest, fits the effective quasi de Sitter prediction as well as the experimental value. This is a result that is model independent and only based on the quantum features of the family of de Sitter vacua.
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A promising candidate for cold dark matter is primordial black holes (PBH) formed from strong primordial quantum fluctuations. A necessary condition for the formation of PBHs is a change of sign in the tilt governing the anomalous scale invariance of the power spectrum from red at large scales into blue at small scales. Non-perturbative information on the dependence of the power spectrum tilt on energy scale can be extracted from the quantum Fisher information measuring the energy dependence of the quantum phases defining the de Sitter vacua. We show that this non-perturbative quantum tilt goes from a red tilted phase, at large scales, into a blue tilted phase at small scales converging to $n_s=2$ in the UV. This allows the formation of PBHs in the range of masses $lesssim 10^{20} gr$.
We provide a unified description of cosmological $alpha$-attractors and late-time acceleration, in excellent agreement with the latest Planck data. Our construction involves two superfields playing distinctive roles: one is the dynamical field and its evolution determines inflation and dark energy, the other is nilpotent and responsible for a landscape of vacua and supersymmetry breaking. We prove that the attractor nature of the theory is enhanced when combining the two sectors: cosmological attractors are very stable with respect to any possible value of the cosmological constant and, interestingly, to any generic coupling of the inflationary sector with the field responsible for uplifting. Finally, as related result, we show how specific couplings generate an arbitrary inflaton potential in a supergravity framework with varying Kahler curvature.
Quantum consistency suggests that any de Sitter patch that lasts a number of Hubble times that exceeds its Gibbons-Hawking entropy divided by the number of light particle species suffers an effect of quantum breaking. Inclusion of other interactions makes the quantum break-time shorter. The requirement that this must not happen puts severe constraints on scalar potentials, essentially suppressing the self-reproduction regimes. In particular, it eliminates both local and global minima with positive energy densities and imposes a general upper bound on the number of e-foldings in any given Hubble patch. Consequently, maxima and other tachyonic directions must be curved stronger than the corresponding Hubble parameter. We show that the key relations of the recently-proposed de Sitter swampland conjecture follow from the de Sitter quantum breaking bound. We give a general derivation and also illustrate this on a concrete example of $D$-brane inflation. We can say that string theory as a consistent theory of quantum gravity nullifies a positive vacuum energy in self-defense against quantum breaking.
In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theory of axion field arising from Type IIB string theory compactified to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For massless axion field, in all these three formalism, we reproduce, at the leading order, the exact scale-invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field, we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in the near future, if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.
We study the arguments given in [1] which suggest that the uplifting procedure in the KKLT construction is not valid. First we show that the modification of the SUSY breaking sector of the nilpotent superfield, as proposed in [1], is not consistent with non-linearly realized local supersymmetry of de Sitter supergravity. Keeping this issue aside, we also show that the corresponding bosonic potential does actually describe de Sitter uplifting.
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