Reconstructing the Inflaton Potential---in Principle and in Practice

Andrew R. Liddle; Edmund Copeland; Edward W. Kolb; James E. Lidsey

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Reconstructing the Inflaton Potential---in Principle and in Practice

Edmund Copeland, Edward W. Kolb, Andrew R. Liddle, James E. Lidsey

High Energy Physics - Phenomenology · Submitted 22 Mar 1993

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The authors' main claim We conclude that in practice, a full reconstruction of the functional form of the potential will not be possible within the foreseeable future.

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arXiv IDhep-ph/9303288 (version 1)

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CitationAndrew R. Liddle, Edmund Copeland, Edward W. Kolb, James E. Lidsey. "Reconstructing the Inflaton Potential---in Principle and in Practice." arXiv:hep-ph/9303288 (1993). https://pith.science/paper/6WC2PNOE

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Generalizing the original work by Hodges and Blumenthal, we outline a formalism which allows one, in principle, to reconstruct the potential of the inflaton field from knowledge of the tensor gravitational wave spectrum or the scalar density fluctuation spectrum, with special emphasis on the importance of the tensor spectrum. We provide some illustrative examples of such reconstruction. We then discuss in some detail the question of whether one can use real observations to carry out this procedure. We conclude that in practice, a full reconstruction of the functional form of the potential will not be possible within the foreseeable future. However, with a knowledge of the dark matter components, it should soon be possible to combine intermediate-scale data with measurements of large-scale cosmic microwave background anisotropies to yield useful information regarding the potential.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Generalizing the original work by Hodges and Blumenthal, we outline a formalism which allows one, in principle, to reconstruct the potential of the inflaton field from knowledge of the tensor gravitational wave spectrum or the scalar density fluctuation spectrum, with special emphasis on the importance of the tensor spectrum.	contribution 0.98	0.83	0.05	asserted 0.53
s1	We provide some illustrative examples of such reconstruction.	contribution 0.95	0.87	0.02	asserted 0.98
s2	We then discuss in some detail the question of whether one can use real observations to carry out this procedure.	contribution 0.87	0.63	0.03	unclear 0.85
s3	We conclude that in practice, a full reconstruction of the functional form of the potential will not be possible within the foreseeable future.	limitation 0.58	0.80	0.77	asserted 0.85
s4	However, with a knowledge of the dark matter components, it should soon be possible to combine intermediate-scale data with measurements of large-scale cosmic microwave background anisotropies to yield useful information regarding the potential.	future work 0.60	0.42	0.10	hedged possibility 0.99

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Original abstract

Generalizing the original work by Hodges and Blumenthal, we outline a formalism which allows one, in principle, to reconstruct the potential of the inflaton field from knowledge of the tensor gravitational wave spectrum or the scalar density fluctuation spectrum, with special emphasis on the importance of the tensor spectrum. We provide some illustrative examples of such reconstruction. We then discuss in some detail the question of whether one can use real observations to carry out this procedure. We conclude that in practice, a full reconstruction of the functional form of the potential will not be possible within the foreseeable future. However, with a knowledge of the dark matter components, it should soon be possible to combine intermediate-scale data with measurements of large-scale cosmic microwave background anisotropies to yield useful information regarding the potential.

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References

Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A Class of Exact Single-Field Inflationary Solutions beyond Slow Roll
astro-ph.CO 2026-09 conditional novelty 6.0 of 10

A solvable Abel ansatz yields an exact family of rolling inflaton backgrounds, and one branch lies inside the joint CMB contour with about 54 e-folds of expansion.
Primordial Gravitational Waves in Quadratic Gravity
gr-qc 2025-02 unverdicted novelty 6.0 of 10

In quadratic gravity, the inflationary tensor power spectrum is suppressed by (1 + 2H_*^2/m_gh^2)^{-1}, which restores the standard consistency relation r = -8n_t.
Orbital Inflation: inflating along an angular isometry of field space
hep-th 2019-07 unverdicted novelty 6.0 of 10

Orbital Inflation reconstructs two-field actions with an angular isometry yielding single-field-like predictions that violate consistency relations and allow f_NL from slow-roll suppressed to O(few) depending on entro...
Large slow-roll corrections to the bispectrum of noncanonical inflation
astro-ph.CO 2011-03 accept novelty 6.0 of 10

The next-order slow-roll corrections to the inflationary bispectrum for general P(X,phi) Lagrangians are derived in closed form, yielding tens-of-percent corrections in DBI inflation and a new bispectrum shape orthogo...
The consistency equation hierarchy in single-field inflation models
astro-ph 2006-03 accept novelty 6.0 of 10

The known consistency relation of single-field inflation is the first of an infinite hierarchy, and the Chung-Shiu-Trodden approximate relation is exactly the second member of that hierarchy.

Show 5 more citing papers

Horizon crossing and inflation with large \eta
gr-qc 2005-03 conditional novelty 6.0 of 10

The horizon-crossing shortcut for inflationary perturbations is valid only when a specific background relation vanishes; a flat-potential model with eta = 3 violates it yet still gives a scale-invariant spectrum.
Model-independent reconstruction of $f(T)$ gravity from Gaussian Processes
astro-ph.CO 2019-07 conditional novelty 5.0 of 10

A model-independent Gaussian-process reconstruction of the f(T) gravity function from Hubble data finds a mean curve close to a cosmological constant with a small quadratic correction.
Bayesian Analysis of Inflation II: Model Selection and Constraints on Reheating
astro-ph.CO 2011-12 conditional novelty 5.0 of 10

Bayesian evidence from WMAP7 and a simulated Planck likelihood shows that neither dataset can single out one simple inflation model, though Planck will exclude multi-regime branches and constrain reheating.
Evolution of fNL to the adiabatic limit
astro-ph.CO 2011-06 conditional novelty 5.0 of 10

In multi-field inflation the asymptotic local fNL is not fixed by the potential alone: it depends on when slow-roll breaks down and on the reheating timescale, and ridge versus valley dynamics leave opposite signs.
Duality Invariance of Cosmological Perturbation Spectra
gr-qc 1998-09 conditional novelty 5.0 of 10

A two-parameter transformation of the cosmological scale factor leaves the spectral index of scalar and tensor perturbations unchanged, relating slow-roll inflation to far-from-slow-roll and collapsing cosmologies.

How the literature uses it

24 arXiv papers cite this in 34 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 15 sentences without a confident label

Uses its method or tool 4 papers

This Hamilton–Jacobi approach to functional reconstruction was developed in [ref] , and it is possible to use it to reconstruct the Jordan frame potential if the form of non-minimal coupling is known.

$\beta$-function reconstruction of Palatini inflationary attractors · Introduction · 0.83
Here we apply the Hamilton-Jacobi formalism [ref] to derive the potential for shift-symmetric orbital inflation, replacing the potential as an input function with the Hubble parameter $H(ϕ)$ which leads directly to the inflation dynamics.

Shift-Symmetric Orbital Inflation: single field or multi-field? · Appendix A. Hamilton-Jacobi Formalism · 0.99
Power spectrum First we quantify the naturalness of $V$ as a slow-roll inflaton potential using the parameters described in [ref] .

A bulk inflaton from large volume extra dimensions · A slow-roll model · 0.93

Cites it as background 12 papers

Reconstruction of the inflationary potential for models of the form ([ref]) has been studied extensively [ref] .

Reconstructing Single Field Inflationary Actions From CMBR Data · Introduction · 0.95
Cosmic inflation also predicts the existence of tensor fluctuations (primordial gravitational waves) whose power spectrum is parameterized, as in the case of the scalar curvature perturbations, by the index $n_t$ and the amplitude $A_t$ [ref] .

Primordial Gravitational Waves in Quadratic Gravity · Introduction · 0.96
Such a mapping exists in the framework of single field, canonical inflation under the slow roll approximation, and the program of reconstruction has been extensively developed [ref] .

Optimizing future experimental probes of inflation · Introduction · 0.84

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