The degeneracy problem in non-canonical inflation

Abstract

While attempting to connect inflationary theories to observational physics, a potential difficulty is the degeneracy problem: a single set of observables maps to a range of different inflaton potentials. Two important classes of models affected by the degeneracy problem are canonical and non-canonical models, the latter marked by the presence of a non-standard kinetic term that generates observables beyond the scalar and tensor two-point functions on CMB scales. The degeneracy problem is manifest when these distinguishing observables go undetected. We quantify the size of the resulting degeneracy in this case by studying the most well-motivated non-canonical theory having Dirac-Born-Infeld Lagrangian. Beyond the scalar and tensor two-point functions on CMB scales, we then consider the possible detection of equilateral non-Gaussianity at Planck-precision and a measurement of primordial gravitational waves from prospective space-based laser interferometers. The former detection breaks the degeneracy with canonical inflation but results in poor reconstruction prospects, while the latter measurement enables a determination of n T which, while not breaking the degeneracy, can be shown to greatly improve the non-canonical reconstruction. †

Features and new physical scales in primordial observables: Theory and observation

“…This term contributes the usual renormalizations of the couplings of our theory and the effective potential. That is to say, bringing this contribution over to the left hand side of (B.7), when M 2 (φ) varies slowly enough we find the usual CW correction lxxxix : 12) which evidently captures the variation of the vacuum energy density of the ψ field along the inflaton trajectory. The second term in (B.11) corresponds to a phase associated with each excited wave number.…”

“…Although one can invoke some selective criteria of 'inference to best theory' [9] to take the current set of observations as confirmation of the inflationary paradigm, it needn't be too much of a stretch to probe the available observations for further evidence before declaring a particular class of inflationary models as the true description of the very early universe. Furthermore, given the large degeneracies that exist between the predictions of different models [10][11][12] (even drastically different cosmologies [13]) at the level of the primordial power spectrum, one might ask, are there any other handles on the data that increase our ability to discriminate between these, or even test the very inflationary paradigm itself?…”

Primordial non-Gaussianity in noncanonical warm inflation

“…However, noncanonical field with a general form of Lagrangian density L = L(X, φ) can generalize the scope of * Electronic address: zhangxm@mail.bnu.edu.cn † Corresponding author; Electronic address: zhujy@bnu.edu.cn inflation, where L(X, φ) is an arbitrary function of the inflaton φ and the kinetic term X that satisfied the conditions proposed in [15]. Much work have been done in the context of the noncanonical standard inflation [15][16][17][18][19][20][21][22][23] and a lot of novel phenomena have been revealed, such as the less restricted slowroll conditions, the usual sub-light 'sound speed' (denotes as c s ) for inflaton scalar perturbations, the modified expression of power spectrum and consistency equation, and in particular significant non-Gaussianity [24]. As far as we know, the warm inflation is always dealt with the canonical fields except in [25] where a warm Dirac-Born-Infeld (DBI) inflationary model was proposed.…”

“…Although the inflation is a successful and elegant picture to explain the problem of horizon, flatness and large scale structure of the Universe etc, there still exists a degeneracy problem [22], i.e. a single set of observables maps to a range of different inflaton models (canonical and noncanonical fields with different potentials).…”

Two-field inflation with non-minimal coupling

“…The standard slow-roll inflationary paradigm, which can give rise to the primordial perturbations, has been emerged as a solution of cosmological problems, namely, flatness, homogeneity, and isotropy problems [1]. Observational precision has been dramatically improved recently [2][3][4][5][6] and the refined understanding of the origin of inflation would be hoped even though there exists degeneracy problem [7]. Some of the key measurements toward the origin of the inflation are the scalar spectral index, n ζ , the tensor-to-scalar ratio, r, and the primordial non-Gaussianity (NG), f NL .…”