Abstract
We study the effect of noncommutative spacetime geometry on one-loop corrections to the primordial curvature two-point function, arising from various forms of massless spectator matter fields interacting gravitationally with the inflaton. After deforming the algebra of functions on the inflationary background to a spatially noncommutative one, we find that this induces momentum-dependent corrections to one-loop terms which imply that the vacuum fluctuation of the energy-momentum tensor sources that of the curvature fluctuation even for distances beyond horizon scales. The one-loop corrections break spatial isotropy by being functions of the noncommutative parameters lying in the tranverse plane while reducing smoothly to the commutative limit. This furnishes an example of how UV/IR mixing manifests itself in the context of noncommutative field theories defined on inflationary backgrounds, and demonstrates how in principle, the primordial spectrum could carry a signature of nonlocality and anisotropy in the setting of noncommutative spacetime geometry.
Highlights
For the primordial universe where quantum gravitational effects were very strong, the notion of a classical spacetime continuum should break down at some point and stringy effects could be dominant in such an era
Noncommutative spacetime geometry can emerge in various settings, a few examples being: (i) a collection of D0 branes in the presence of external Ramond-Ramond (RR) fourform flux expanding into a noncommutative S2 [3], (ii) vertex operators of open strings following an associative but noncommutative Moyal star product in the presence of a large Neveu-Schwarz-Neveu-Schwarz (NS-NS) B-field B in the zero slope (α0 → 0) limit, with the target space coordinates obeying a noncommutative bracket [4]
Studying issues of how noncommutative geometry could potentially manifest itself in primordial cosmology especially in the context of inflationary dynamics [5,6,7,8]
Summary
For the primordial universe where quantum gravitational effects were very strong, the notion of a classical spacetime continuum should break down at some point and stringy effects could be dominant in such an era. We consider one-loop corrections to primordial spectrum arising from massless matter fields that interact purely gravitationally with the inflaton coupled with the backdrop that they reside on a noncommutative spacetime, in this case, a slow-roll inflationary background. Iij is a matrix equal to Æ1 depending on whether the line j (with momentum kj) crosses line i (with momentum ki) from the right or left respectively, being zero in the absence of crossing, and θ is the noncommutative constant matrix-valued parameter We perform this calculation in the comoving curvature gauge (in which inflaton fluctuations are set to zero) for the cases of massless scalars, fermions and U(1) gauge fields.
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