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In this work, we study the key role of generic Effective Field Theory (EFT) framework to quantify the correlation functions in a quasi de Sitter background for an arbitrary initial choice of the quantum vacuum state. We perform the computation in unitary gauge in which we apply Stu¨ckelberg trick in lowest dimensional EFT operators which are broken under time diffeomorphism. Particularly using this non-linear realization of broken time diffeomorphism and truncating the action by considering the contribution from two derivative terms in the metric we compute the two point and three point correlations from scalar perturbations and two-point correlation from tensor perturbations to quantify the quantum fluctuations observed in Cosmic Microwave Background (CMB) map. We also use equilateral limit and squeezed limit configurations for the scalar three-point correlations in Fourier space. To give future predictions from EFT setup and to check the consistency of our derived results for correlations, we use the results obtained from all class of the canonical single field and general single field P(X,ϕ) model. This analysis helps us to fix the coefficients of the relevant operators in EFT in terms of the slow roll parameters and effective sound speed. Finally, using CMB observation from Planck we constrain all of these coefficients of EFT operators for single field slow roll inflationary paradigm.

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It has been conjectured that fermions minimally coupled to a Chern-Simons gauge field define a conformal field theory (CFT) that is level-rank dual to Chern-Simons gauged Wilson-Fisher Bosons. The CFTs in question admit relevant deformations parametrized by a real mass. When the mass deformation is positive, the duality of the two deformed theories has previously been checked in detail in the large N limit by comparing explicit all orders results on both sides of the duality. In this paper, we perform a similar check for the case of negative mass deformations. In this case, the bosonic field condenses triggering the Higgs mechanism. The effective excitations in this phase are massive W bosons. By summing all leading large N graphs involving these W bosons we find an all orders (in the 't Hooft coupling) result for the thermal free energy of the bosonic theory in the condensed phase. Our final answer perfectly matches the previously obtained fermionic free energy under the conjectured duality map.

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We investigate for an Effective Field Theory (EFT) framework that can consistently explain inflation to Large Scale Structures (LSS). With the development of the construction algorithm of EFT, we arrive at a properly truncated action for the entire scenario. Using this, we compute the two-point correlation function for quantum fluctuations from Goldstone modes and related inflationary observables in terms of coefficients of relevant EFT operators, which we constrain using Planck 2015 data. We then carry forward this primordial power spectrum with the same set of EFT parameters to explain the linear and non-linear regimes of LSS by loop-calculations of the matter overdensity two-point function. For comparative analysis, we make use of two widely accepted transfer functions, namely, BBKS and Eisenstein-Hu, thereby making the analysis robust. We finally corroborate our results with LSS data from SDSS-DR7 and WiggleZ. The analysis thus results in a consistent, model-independent EFT framework for inflation to structures.

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In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergravity, extra-dimensional theory, modified gravity etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description, we have restricted our analysis for two scalar fields - dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R^2 gravity, from which we have studied the attractor and non-attractor phase by exactly computing two point, three point and four point correlation functions from scalar fluctuations using In-In (Schwinger-Keldysh) and δ formalism. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter collinear) of the amplitude as obtained from three and four-point scalar functions, which are consistent with observed data. Also, the results from two-point tensor fluctuations and field excursion formula are explicitly presented for attractor and non-attractor phase. Further, reheating constraints, the scale-dependent behavior of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness.

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In this article, we propose different background models of extended theories of gravity, which are minimally coupled to the SM fields, to explain the possibility of the genesis of dark matter without affecting the SM particle sector. We modify the gravity sector by allowing quantum corrections motivated from (1) local f(R) gravity and (2) non-minimally coupled gravity with SM sector and dilaton field. Next, we apply a conformal transformation on the metric to transform the action back to the Einstein frame. We also show that an effective theory constructed from these extended theories of gravity and SM sector looks exactly the same. Using the relic constraint observed by Planck 2015, we constrain the scale of the effective field theory (ΛUV) as well as the dark matter mass (M). We consider two cases- (1) light dark matter (LDM) and (2) heavy dark matter (HDM) and deduce upper bounds on the thermally averaged cross section of dark matter annihilating to SM particles. Further, we show that our model naturally incorporates self-interactions of dark matter. Using these self-interactions, we derive the constraints on the parameters of the (1) local f(R) gravity and (2) non-minimally coupled gravity from dark matter self-interaction. Finally, we propose some different UV complete models from a particle physics point of view, which can give rise to the same effective theory that we have deduced from extended theories of gravity.

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It has recently been demonstrated that the large N limit of a model of fermions charged under the global/gauge symmetry group O(N)^{q−1} agrees with the large N limit of the SYK model. In these notes, we investigate aspects of the dynamics of the O(N)q−1 theories that differ from their SYK counterparts. We argue that the spectrum of fluctuations about the finite temperature saddle point in these theories has (q−1)N^2/2 new light modes in addition to the light Schwarzian mode that exists even in the SYK model, suggesting that the bulk dual description of theories differ significantly if they both exist. We also study the thermal partition function of a mass deformed version of the SYK model. At-large mass we show that the effective entropy of this theory grows with energy like ElnE (i.e. faster than Hagedorn) up to energies of order N2. The canonical partition function of the model displays a deconfinement or Hawking Page type phase transition at temperatures of order 1/lnN. We derive these results in the large mass limit but argue that they are qualitatively robust to small corrections in J/m.

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In this work, we have studied the possibility of setting up Bell's inequality violating experiment in the context of cosmology, based on the basic principles of quantum mechanics. First we start with the physical motivation of implementing the Bell's inequality violation in the context of cosmology. Then to set up the cosmological Bell violating test experiment we introduce a model independent theoretical framework using which we have studied the creation of new massive particles by implementing the WKB approximation method for the scalar fluctuations in presence of additional time-dependent mass contribution. Next using the background scalar fluctuation in presence of new time-dependent mass contribution, we explicitly compute the expression for the one point and two-point correlation functions. Furthermore, using the results for one point function we introduce a new theoretical cosmological parameter which can be expressed in terms of the other known inflationary observables and can also be treated as a future theoretical probe to break the degeneracy amongst various models of inflation. Additionally, we also fix the scale of inflation in a model independent way without any prior knowledge of primordial gravitational waves. Next, we also comment on the technicalities of measurements from isospin breaking interactions and the future prospects of newly introduced massive particles in cosmological Bell violating test experiment. Further, we cite a precise example of this set up applicable in the context of string theory motivated axion monodromy model. Then we comment on the explicit role of decoherence effect and high spin on cosmological Bell violating test experiment. In fine, we provide a theoretical bound on the heavy particle mass parameter for scalar fields, graviton and other high spin fields from our proposed setup.

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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 in presence of axion originating from {\bf Type IIB} string theory. Compared to the usual approach followed in (primordial) cosmology here we use most elegant and technically correct methods to compute the expression for the power spectrum of vacuum fluctuation. For this computation, we consider two causally separated region ({\bf L} and {\bf R}) in open hyperbolic chart of the de Sitter space-time. We start our analysis with three approaches -1. field operator expansion (FOE) technique with the quantum entangled state, 2. reduced density matrix (RDM) formalism with mixed quantum state and 3. non-entangled state (NES) method. For FOE and RDM we are tracing out the physical information from of one of the regions ({\bf R} ) and for NES we consider the Hilbert space is only described by region {\bf L} in de Sitter hyperbolic open chart. For massless ($\nu=3/2$) axion field we get the exact scale invariant feature of the power spectrum on small scale from this three formalism at the leading order which is consistent with the finding of the observational probes for early universe cosmology. Additionally, we due to quantum entanglement we get different quantum correction terms in the power spectrum for these thee formalisms at the next to leading order. Such correction terms serve the purpose of the breaking of degeneracy among the outcomes of the FOE, RDM and NES formalisms in the superhorizon limit. On the other hand, for massive ($\nu\neq 3/2$) axion filed 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 ($\nu=3/2$) and massive ($\nu=3/2$) axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the outcome of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of de Sitter space.

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