# Constraints on Inflation (Planck 2015 results XX)

Gold Member
Dearly Missed
An interesting dimension of the Planck results that can use a thread on its own.

http://www.cosmos.esa.int/documents/387566/522789/Planck_2015_Results_XX_Constraints_Inflation.pdf/
Planck 2015 results. XX. Constraints on inflation
Preprint online version: February 7, 2015

ABSTRACT

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 Release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be ns = 0.968 ± 0.006 and tightly constrain its scale dependence to dns/d ln k = −0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-l polarization data is included, the results are consistent and uncertainties are further reduced.
The upper bound on the tensor-to-scalar ratio is r0.002 < 0.11 (95%CL).
This upper limit is consistent with the B-mode polarization constraint r < 0.12 (95 % CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data.
These results imply that V (φ) ∝ φ2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R2 inflation.
We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth PR(k) over the range of scales 0.008 Mpc−1 < k < 0.1 Mpc−1. At large scales, each method finds deviations from a power law, connected to a deficit at multipoles l ≈ 20–40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base ΛCDM model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95 % CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is |αnon-adi | < 1.9 %, 4.0 %, and 2.9 % for cold dark matter (CDM), neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum finding that the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. These results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.
==endquote==

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Chalnoth
It is kind of cool that the Natural Inflation models seem to be disfavored. Natural Inflation is essentially the most generic possible inflation model: any irregular potential energy function will be shaped like $\phi^2$ near its minimum. This means that if we had detected Natural Inflation, it would have meant very little for the details of the physics that produced inflation.

If Natural Inflation isn't correct, then that means that if we ever do nail down the proper model for the pre-big bang universe, we are more likely to be able to extract some interesting information out of it.

cristo
Haelfix
It is kind of cool that the Natural Inflation models seem to be disfavored. Natural Inflation is essentially the most generic possible inflation model: any irregular potential energy function will be shaped like $\phi^2$ near its minimum. This means that if we had detected Natural Inflation, it would have meant very little for the details of the physics that produced inflation.
Yes this is true, although in some sense the old values of Bicep were particularly nice, b/c there wasn't a great deal of degeneracy within the space of inflationary potentials. That particular spot in the r-ns plane was much more predictive than where the great glut of model predictions happen to be centered (eg much lower values of the scalar to tensor ratio).

From a theory perspective the old value's also implied some rather fascinating bounds, and was in tension with naive effective field theory arguments (you either pushed up against the so called Lyth bound and had tension with finetuning and/or the weak gravity conjecture) or you had to deal with a large amount of particle species (axion monodromy).

Unfortunately, the way things are headed will require quite a bit more precision to really tease out a particular model, which might take a very long time to accomplish.

bapowell
It is kind of cool that the Natural Inflation models seem to be disfavored. Natural Inflation is essentially the most generic possible inflation model: any irregular potential energy function will be shaped like $\phi^2$ near its minimum. This means that if we had detected Natural Inflation, it would have meant very little for the details of the physics that produced inflation.

If Natural Inflation isn't correct, then that means that if we ever do nail down the proper model for the pre-big bang universe, we are more likely to be able to extract some interesting information out of it.
Natural inflation can also be modeled as an inverted potential, going as $1 - \phi^2$ near the local maximum. This form is not quite as generic -- while it is the lowest-order Taylor approximation of many irregular inverted potentials, those with suppressed mass terms (for example, within the context of certain PNGB models), are instead given by $1 - \phi^4$ near the maximum. These are examples of natural inflation models that are still in the running....

Gold Member
Dearly Missed
Hi Brian, Haelfix, Chalnoth,
I am especially interested in seeing how the observational constraints on inflation can be brought to bear on the main alternative scenarios which I see being studied. The challenges and problems with MBS (matter bounce scenarios) in the light of the latest Planck mission results were just recently reviewed by Jaume de Haro and Yi-fu Cai.
Let's see what they said:
http://inspirehep.net/record/1343988
An Extended Matter Bounce Scenario: current status and challenges
Jaume de Haro, Yi-Fu Cai
Feb 11, 2015
e-Print: arXiv:1502.03230 [gr-qc] | PDF
Abstract (arXiv)
As an alternative to the paradigm of slow roll inflation, we propose an extended scenario of the matter bounce cosmology in which the Universe has experienced a quasi-matter contracting phase with a variable background equation of state parameter. This extended matter bounce scenario can be realized by considering a single scalar field evolving along an approximately exponential potential. Our result reveals that the rolling of the scalar field in general leads to a running behavior on the spectral index of primordial cosmological perturbations and a negative running can be realized in this model. We constrain the corresponding parameter space by using the newly released Planck data. To apply this scenario, we revisit bouncing cosmologies within the context of modified gravity theories, in particular, the holonomy corrected loop quantum cosmology and teleparallel F(T) gravity. A gravitational process of reheating is presented in such a matter bounce scenario to demonstrate the condition of satisfying current observations. We also comment on several unresolved issues that often appear in matter bounce models.

bapowell
A main issue here is the degeneracy problem -- how can we distinguish the matter bounce scenario from inflation? I believe the generic matter bounce gives a tensor spectrum with zero tilt, but future surveys likely won't be able to distinguish the zero tilt from the small tilt expected from simple single field inflation models.

Gold Member
Dearly Missed
A main issue here is the degeneracy problem -- how can we distinguish the matter bounce scenario from inflation?
Definitely!
If both MBS and an inflation scenario fit the observational data we have so far, what additional tests can be made to discriminate between them. Cai&deHaro outline 7 important issues constraining both inflation scenarios and MBS. It is a useful survey, I think
==excerpt C&dH==
In order to obtain a viable MBS model that can compete with the inflationary paradigm, it is expected that the underlying model can satisfy a variety of theoret- ical and observational constraints. Moreover, there exist several conceptual issues that are not clear in the frame of the MBS. We list these points in the following and discuss the conditions of model building in the MBS in the present work.

First, today’s cosmological measurements, such as the Planck data released in 2013 (Planck2013) [9, 10] as well as in 2015 (Planck2015) [11, 12], have precisely determined the amplitude of the power spectrum for primordial curvature perturbations to be Pξ ≅ 2.2 × 10−9. This amplitude, in bounce models, is often associated with the energy scale of the bounce as well as the process of primordial perturbations evolving through the nonsingular bouncing phase [13]. ..

Second, according to the Planck2015 data, at 1σ confidence level (C.L.) the spectral index for curvature perturbation and its running, namely, ns and αs, are constrained to be 0.968 ± 0.006 and −0.003 ± 0.007...

Third, it is important to take into account the observational constraint of primordial non-gaussianity upon early Universe models. So far there is no evidence pointing to the existence of these nonlinear fluctuations [15, 16]. As a result a large number of inflation models are ruled out by this observational fact. Thus, the no-detection of primordial non-gaussianity is expected to tightly constrain bounce models. For instance, it was studied in detail in ...

Fourth, the latest CMB experiments including the BICEP2/Keck Array and Planck data have constrained the tensor-to-scalar ratio to be r ≤ 0.12 with a pivot scale of 0.05 Mpc−1 at 2σ C.L. [19]. When applied to inflation models, ... it requires the inflaton’s potential to be very flat and hence indicates a fine tuning issue [21]. In the simplest model of MBS, the amplitude of tensor fluctuation is comparable to that of curvature perturbation and thus the value of r is too large [22]. Accordingly, one may expect certain dynamical mechanisms to be implemented in the MBS ... Also, it is possible to consider the effects of modified gravity ...to depress gravitational waves during the bounce [24]. Therefore, the no-detection of primordial gravitational waves can also impose a bound on various bounce models.

Fifth, a Universe whose background dynamics is realized by a primordial scalar field ... has to reheat via decaying into light particles that will thermalize to match with the standard hot big bang expansion. Reheating could be produced due to the gravitational particle creation in an expanding Universe [25, 26]. .. In bouncing cosmologies, the gravitational particle creation is natural to be implemented since the Universe would have experienced several phases including contracting, bouncing and expanding ones [27], and then, it is necessary to examine whether the reheating temperature is compatible with the current data [28].

Sixth, bouncing cosmologies often suffer from a dangerous growth of primordial anisotropy of which the effective energy density scales as a−6 in contracting phase. This is known as the famous Belinsky-Khalatnikov-Lifshitz (BKL) instability [29]. A solution to this problem can be realized in ... However, it is important to be aware of this issue in other mechanisms of nonsingular bounces, such as taking into account nonlinear matter contribution to smooth out the anisotropies [33]
==endquote==
They also list a seventh which is the cosmological constant issue, how well do various models accommodate late time acceleration?

Brian, I'm hoping that somewhere in this list of different kinds of constraints, most of which seem to affect both MBS and inflation scenarios, an answer to your question about degeneracy (how to discriminate?) will show up.

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Chalnoth
Hi Brian, Haelfix, Chalnoth,
I am especially interested in seeing how the observational constraints on inflation can be brought to bear on the main alternative scenarios which I see being studied. The challenges and problems with MBS (matter bounce scenarios) in the light of the latest Planck mission results were just recently reviewed by Jaume de Haro and Yi-fu Cai.
Let's see what they said:
http://inspirehep.net/record/1343988
An Extended Matter Bounce Scenario: current status and challenges
Jaume de Haro, Yi-Fu Cai
Feb 11, 2015
e-Print: arXiv:1502.03230 [gr-qc] | PDF
Abstract (arXiv)
As an alternative to the paradigm of slow roll inflation, we propose an extended scenario of the matter bounce cosmology in which the Universe has experienced a quasi-matter contracting phase with a variable background equation of state parameter. This extended matter bounce scenario can be realized by considering a single scalar field evolving along an approximately exponential potential. Our result reveals that the rolling of the scalar field in general leads to a running behavior on the spectral index of primordial cosmological perturbations and a negative running can be realized in this model. We constrain the corresponding parameter space by using the newly released Planck data. To apply this scenario, we revisit bouncing cosmologies within the context of modified gravity theories, in particular, the holonomy corrected loop quantum cosmology and teleparallel F(T) gravity. A gravitational process of reheating is presented in such a matter bounce scenario to demonstrate the condition of satisfying current observations. We also comment on several unresolved issues that often appear in matter bounce models.
Personally, I've been rather uninterested in understanding the details of this very much. I figure it will make a difference when we have a CMB satellite designed to observe polarization, but until then we just can't say much one way or the other about any inflation models.

A ground or balloon-based observation might get us partway there, but we really need a new satellite to have good information on the matter.