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Title: Observational Constraints on the Tilted Spatially Flat and the Untilted Nonflat $$\phi$$CDM Dynamical Dark Energy Inflation Models

Abstract

Herein we constrain spatially flat tilted and nonflat untilted scalar field ($$\phi$$) dynamical dark energy inflation ($$\phi$$CDM) models by using Planck 2015 cosmic microwave background (CMB) anisotropy measurements and recent baryonic acoustic oscillation distance observations, Type Ia supernovae apparent magnitude data, Hubble parameter measurements, and growth rate data. We assume an inverse power-law scalar field potential energy density $$V(\phi )={V}_{0}{\phi }^{-\alpha }$$. We find that the combination of the CMB data with the four non-CMB data sets significantly improves parameter constraints and strengthens the evidence for nonflatness in the nonflat untilted $$\phi$$CDM case from 1.8$$σ$$ for the CMB measurements only to more than 3.1$$σ$$ for the combined data. In the nonflat untilted $$\phi$$CDM model, current observations favor a spatially closed universe with spatial curvature contributing about two-thirds of a percent of the present cosmological energy budget. The flat tilted $$\phi$$CDM model is a 0.4$$σ$$ better fit to the data than is the standard flat tilted $$Λ$$CDM model: current data allow for the possibility that dark energy is dynamical. The nonflat tilted $$\phi$$CDM model is in better accord with the Dark Energy Survey bounds on the rms amplitude of mass fluctuations now ($$σ_8$$) as a function of the nonrelativistic matter density parameter now ($$Ω_m$$) but it does not provide as good a fit to the larger-multipole Planck 2015 CMB anisotropy data as does the standard flat tilted $$Λ$$CDM model. A few cosmological parameter value measurements differ significantly when determined using the tilted flat and the untilted nonflat $$\phi$$CDM models, including the cold dark matter density parameter and the reionization optical depth.

Authors:
 [1]; ORCiD logo [2]
  1. Chonbuk National Univ., Jeonju (Republic of Korea); Kansas State Univ., Manhattan, KS (United States)
  2. Kansas State Univ., Manhattan, KS (United States)
Publication Date:
Research Org.:
Kansas State Univ., Manhattan, KS (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Research Foundation of Korea (NRF)
OSTI Identifier:
1613082
Alternate Identifier(s):
OSTI ID: 1642537
Grant/Contract Number:  
SC0019038
Resource Type:
Accepted Manuscript
Journal Name:
The Astrophysical Journal (Online)
Additional Journal Information:
Journal Name: The Astrophysical Journal (Online); Journal Volume: 868; Journal Issue: 2; Journal ID: ISSN 1538-4357
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; astronomy & astrophysics; cosmic background radiation; cosmological parameters; inflation; large-scale structure of universe; methods: statistical

Citation Formats

Park, Chan-Gyung, and Ratra, Bharat. Observational Constraints on the Tilted Spatially Flat and the Untilted Nonflat $\phi$CDM Dynamical Dark Energy Inflation Models. United States: N. p., 2018. Web. doi:10.3847/1538-4357/aae82d.
Park, Chan-Gyung, & Ratra, Bharat. Observational Constraints on the Tilted Spatially Flat and the Untilted Nonflat $\phi$CDM Dynamical Dark Energy Inflation Models. United States. https://doi.org/10.3847/1538-4357/aae82d
Park, Chan-Gyung, and Ratra, Bharat. Mon . "Observational Constraints on the Tilted Spatially Flat and the Untilted Nonflat $\phi$CDM Dynamical Dark Energy Inflation Models". United States. https://doi.org/10.3847/1538-4357/aae82d. https://www.osti.gov/servlets/purl/1613082.
@article{osti_1613082,
title = {Observational Constraints on the Tilted Spatially Flat and the Untilted Nonflat $\phi$CDM Dynamical Dark Energy Inflation Models},
author = {Park, Chan-Gyung and Ratra, Bharat},
abstractNote = {Herein we constrain spatially flat tilted and nonflat untilted scalar field ($\phi$) dynamical dark energy inflation ($\phi$CDM) models by using Planck 2015 cosmic microwave background (CMB) anisotropy measurements and recent baryonic acoustic oscillation distance observations, Type Ia supernovae apparent magnitude data, Hubble parameter measurements, and growth rate data. We assume an inverse power-law scalar field potential energy density $V(\phi )={V}_{0}{\phi }^{-\alpha }$. We find that the combination of the CMB data with the four non-CMB data sets significantly improves parameter constraints and strengthens the evidence for nonflatness in the nonflat untilted $\phi$CDM case from 1.8$σ$ for the CMB measurements only to more than 3.1$σ$ for the combined data. In the nonflat untilted $\phi$CDM model, current observations favor a spatially closed universe with spatial curvature contributing about two-thirds of a percent of the present cosmological energy budget. The flat tilted $\phi$CDM model is a 0.4$σ$ better fit to the data than is the standard flat tilted $Λ$CDM model: current data allow for the possibility that dark energy is dynamical. The nonflat tilted $\phi$CDM model is in better accord with the Dark Energy Survey bounds on the rms amplitude of mass fluctuations now ($σ_8$) as a function of the nonrelativistic matter density parameter now ($Ω_m$) but it does not provide as good a fit to the larger-multipole Planck 2015 CMB anisotropy data as does the standard flat tilted $Λ$CDM model. A few cosmological parameter value measurements differ significantly when determined using the tilted flat and the untilted nonflat $\phi$CDM models, including the cold dark matter density parameter and the reionization optical depth.},
doi = {10.3847/1538-4357/aae82d},
journal = {The Astrophysical Journal (Online)},
number = 2,
volume = 868,
place = {United States},
year = {Mon Nov 26 00:00:00 EST 2018},
month = {Mon Nov 26 00:00:00 EST 2018}
}

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Works referenced in this record:

Cosmographic bounds on the cosmological deceleration-acceleration transition redshift in f ( R ) gravity
journal, August 2014


Conservative constraints on early cosmology with M ONTE P YTHON
journal, February 2013

  • Audren, Benjamin; Lesgourgues, Julien; Benabed, Karim
  • Journal of Cosmology and Astroparticle Physics, Vol. 2013, Issue 02
  • DOI: 10.1088/1475-7516/2013/02/001

Measuring the Hubble constant with Type Ia supernovae as near-infrared standard candles
journal, January 2018


Should Type Ia Supernova Distances Be Corrected for Their Local Environments?
journal, November 2018


New Model-Independent Method to test the Curvature of the Universe
journal, September 2016


A Measurement of the Hubble Constant Using Galaxy Redshift Surveys
journal, November 2017


An Improved Method to Measure the Cosmic Curvature
journal, April 2017


Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann‐Robertson‐Walker Models
journal, August 2000

  • Lewis, Antony; Challinor, Anthony; Lasenby, Anthony
  • The Astrophysical Journal, Vol. 538, Issue 2
  • DOI: 10.1086/309179

Environmental Dependence of Type Ia Supernova Luminosities from a Sample without a Local–Global Difference in Host Star Formation
journal, February 2018

  • Kim, Young-Lo; Smith, Mathew; Sullivan, Mark
  • The Astrophysical Journal, Vol. 854, Issue 1
  • DOI: 10.3847/1538-4357/aaa127

Planck 2015 Constraints on the Non-flat ΛCDM Inflation Model
journal, August 2018

  • Ooba, Junpei; Ratra, Bharat; Sugiyama, Naoshi
  • The Astrophysical Journal, Vol. 864, Issue 1
  • DOI: 10.3847/1538-4357/aad633

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: first measurement of baryon acoustic oscillations between redshift 0.8 and 2.2
journal, October 2017

  • Ata, Metin; Baumgarten, Falk; Bautista, Julian
  • Monthly Notices of the Royal Astronomical Society, Vol. 473, Issue 4
  • DOI: 10.1093/mnras/stx2630

An improved model-independent assessment of the late-time cosmic expansion
journal, October 2018

  • Haridasu, Balakrishna S.; Luković, Vladimir V.; Moresco, Michele
  • Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 10
  • DOI: 10.1088/1475-7516/2018/10/015

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
journal, March 2017

  • Alam, Shadab; Ata, Metin; Bailey, Stephen
  • Monthly Notices of the Royal Astronomical Society, Vol. 470, Issue 3
  • DOI: 10.1093/mnras/stx721

Constraints on dark energy dynamics and spatial curvature from Hubble parameter and baryon acoustic oscillation data
journal, July 2018

  • Ryan, Joseph; Doshi, Sanket; Ratra, Bharat
  • Monthly Notices of the Royal Astronomical Society, Vol. 480, Issue 1
  • DOI: 10.1093/mnras/sty1922

Dynamical dark energy vs. Λ = const in light of observations
journal, February 2018

  • Solà Peracaula, Joan; de Cruz Pérez, Javier; Gómez-Valent, Adrià
  • EPL (Europhysics Letters), Vol. 121, Issue 3
  • DOI: 10.1209/0295-5075/121/39001

Model independent constraints on transition redshift
journal, May 2018

  • Jesus, J. F.; Holanda, R. F. L.; Pereira, S. H.
  • Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 05
  • DOI: 10.1088/1475-7516/2018/05/073

Planck 2015 results : XIII. Cosmological parameters
journal, September 2016


CONFIRMATION OF A STAR FORMATION BIAS IN TYPE Ia SUPERNOVA DISTANCES AND ITS EFFECT ON THE MEASUREMENT OF THE HUBBLE CONSTANT
journal, March 2015


Possible signals of vacuum dynamics in the Universe
journal, May 2018

  • Solà Peracaula, Joan; de Cruz Pérez, Javier; Gómez-Valent, Adrià
  • Monthly Notices of the Royal Astronomical Society, Vol. 478, Issue 4
  • DOI: 10.1093/mnras/sty1253

Hubble Parameter Measurement Constraints on the Redshift of the Deceleration–Acceleration Transition, Dynamical dark Energy, and Space Curvature
journal, January 2017

  • Farooq, Omer; Madiyar, Foram Ranjeet; Crandall, Sara
  • The Astrophysical Journal, Vol. 835, Issue 1
  • DOI: 10.3847/1538-4357/835/1/26

Exploring parameter constraints on quintessential dark energy: The inverse power law model
journal, May 2009


What makes the Universe accelerate? A review on what dark energy could be and how to test it
journal, December 2017


Binned Hubble parameter measurements and the cosmological deceleration–acceleration transition
journal, October 2013


Hints of Dynamical Vacuum Energy in the Expanding Universe
journal, September 2015

  • Solà, Joan; Gómez-Valent, Adrià; de Cruz Pérez, Javier
  • The Astrophysical Journal, Vol. 811, Issue 1
  • DOI: 10.1088/2041-8205/811/1/L14

How well do we understand cosmological recombination?
journal, May 2008


An Evaluation of Cosmological Models from the Expansion and Growth of Structure Measurements
journal, December 2017

  • Zhai, Zhongxu; Blanton, Michael; Slosar, Anže
  • The Astrophysical Journal, Vol. 850, Issue 2
  • DOI: 10.3847/1538-4357/aa9888

Planck 2015 Constraints on the Nonflat ϕ CDM Inflation Model
journal, October 2018

  • Ooba, Junpei; Ratra, Bharat; Sugiyama, Naoshi
  • The Astrophysical Journal, Vol. 866, Issue 1
  • DOI: 10.3847/1538-4357/aadcf3

Dark Energy Survey Year 1 Results: A Precise H0 Estimate from DES Y1, BAO, and D/H Data
journal, July 2018

  • Abbott, T. M. C.; Abdalla, F. B.; Annis, J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 480, Issue 3
  • DOI: 10.1093/mnras/sty1939

A New Calculation of the Recombination Epoch
journal, September 1999

  • Seager, S.; Sasselov, D. D.; Scott, D.
  • The Astrophysical Journal, Vol. 523, Issue 1
  • DOI: 10.1086/312250

Cosmological parameters from CMB and other data: A Monte Carlo approach
journal, November 2002


Everything you always wanted to know about the cosmological constant problem (but were afraid to ask)
journal, July 2012


New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope : Implications for the Hubble Constant
journal, March 2018

  • Riess, Adam G.; Casertano, Stefano; Yuan, Wenlong
  • The Astrophysical Journal, Vol. 855, Issue 2
  • DOI: 10.3847/1538-4357/aaadb7

Isotropic vs. anisotropic components of BAO data: a tool for model selection
journal, May 2018

  • Haridasu, Balakrishna S.; Luković, Vladimir V.; Vittorio, Nicola
  • Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 05
  • DOI: 10.1088/1475-7516/2018/05/033

Galaxy cluster number count data constraints on cosmological parameters
journal, November 2012


Constraining cosmic curvature by using age of galaxies and gravitational lenses
journal, March 2017

  • Rana, Akshay; Jain, Deepak; Mahajan, Shobhit
  • Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 03
  • DOI: 10.1088/1475-7516/2017/03/028

First Evidence of Running Cosmic Vacuum: Challenging the Concordance Model
journal, February 2017

  • Solà, Joan; Gómez-Valent, Adrià; Pérez, Javier de Cruz
  • The Astrophysical Journal, Vol. 836, Issue 1
  • DOI: 10.3847/1538-4357/836/1/43

Cosmological model-independent test of $$\varLambda $$ Λ CDM with two-point diagnostic by the observational Hubble parameter data
journal, April 2018


Cosmology with a time-variable cosmological 'constant'
journal, February 1988

  • Peebles, P. J. E.; Ratra, Bharat
  • The Astrophysical Journal, Vol. 325
  • DOI: 10.1086/185100

Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories
journal, December 2001


Density perturbations for running vacuum: a successful approach to structure formation and to the σ8-tension
journal, April 2018

  • Gómez-Valent, Adrià; Solà Peracaula, Joan
  • Monthly Notices of the Royal Astronomical Society, Vol. 478, Issue 1
  • DOI: 10.1093/mnras/sty1028

Median Statistics and the Hubble Constant
journal, September 2011

  • Chen, Gang; Ratra, Bharat
  • Publications of the Astronomical Society of the Pacific, Vol. 123, Issue 907
  • DOI: 10.1086/662131

Inflation in a closed universe
journal, November 2017


Inflation in an exponential-potential scalar field model
journal, March 1992


Is There Evidence for dark Energy Evolution?
journal, April 2015


Exhaustive study of cosmic microwave background anisotropies in quintessential scenarios
journal, October 2000


The Beginning and Evolution of the Universe
journal, March 2008

  • Ratra, Bharat; Vogeley, Michael S.
  • Publications of the Astronomical Society of the Pacific, Vol. 120, Issue 865
  • DOI: 10.1086/529495

WHAT ARE THE Omh 2 ( z 1 , z 2 ) AND Om ( z 1 , z 2 ) DIAGNOSTICS TELLING US IN LIGHT OF H ( z ) DATA?
journal, June 2016


Dynamical dark energy in light of the latest observations
journal, August 2017


Determining the Hubble Constant from Hubble Parameter Measurements
journal, January 2017


A More Accurate and Competitive Estimative of H0 in Intermediate Redshifts
journal, June 2018


Relaxing the σ 8 -tension through running vacuum in the Universe
journal, November 2017


Dynamical dark energy: Scalar fields and running vacuum
journal, March 2017

  • Solà, Joan; Gómez-Valent, Adrià; de Cruz Pérez, Javier
  • Modern Physics Letters A, Vol. 32, Issue 09
  • DOI: 10.1142/S0217732317500547

Inflation in an open universe
journal, August 1995


First study of reionization in the Planck 2015 normalized closed ΛCDM inflation model
journal, July 2018

  • Mitra, Sourav; Choudhury, Tirthankar Roy; Ratra, Bharat
  • Monthly Notices of the Royal Astronomical Society, Vol. 479, Issue 4
  • DOI: 10.1093/mnras/sty1835

Dependence of Type Ia supernova luminosities on their local environment
journal, July 2018


The H 0 tension in light of vacuum dynamics in the universe
journal, November 2017


Dark Energy Survey year 1 results: Cosmological constraints from galaxy clustering and weak lensing
journal, August 2018


Median Statistics Analysis of Deuterium Abundance Measurements and Spatial Curvature Constraints
journal, September 2018

  • Penton, Jarred; Peyton, Jacob; Zahoor, Aasim
  • Publications of the Astronomical Society of the Pacific, Vol. 130, Issue 993
  • DOI: 10.1088/1538-3873/aadf75

A 6% measurement of the Hubble parameter at z ∼0.45: direct evidence of the epoch of cosmic re-acceleration
journal, May 2016

  • Moresco, Michele; Pozzetti, Lucia; Cimatti, Andrea
  • Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 05
  • DOI: 10.1088/1475-7516/2016/05/014

QUANTIFYING DISCORDANCE IN THE 2015 PLANCK CMB SPECTRUM
journal, February 2016


Median Statistics, H 0 , and the Accelerating Universe
journal, March 2001

  • Gott III, J. Richard; Vogeley, Michael S.; Podariu, Silviu
  • The Astrophysical Journal, Vol. 549, Issue 1
  • DOI: 10.1086/319055

An independent determination of the local Hubble constant
journal, October 2017

  • Fernández Arenas, David; Terlevich, Elena; Terlevich, Roberto
  • Monthly Notices of the Royal Astronomical Society, Vol. 474, Issue 1
  • DOI: 10.1093/mnras/stx2710

Polar Network Index as a Magnetic Proxy for the Solar Cycle Studies
journal, September 2014

  • Priyal, Muthu; Banerjee, Dipankar; Karak, Bidya Binay
  • The Astrophysical Journal, Vol. 793, Issue 1
  • DOI: 10.1088/2041-8205/793/1/L4

Creation of open universes from de Sitter space
journal, January 1982


The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes
journal, July 2011

  • Blas, Diego; Lesgourgues, Julien; Tram, Thomas
  • Journal of Cosmology and Astroparticle Physics, Vol. 2011, Issue 07
  • DOI: 10.1088/1475-7516/2011/07/034

Small‐Scale Cosmological Perturbations: An Analytic Approach
journal, November 1996

  • Hu, Wayne; Sugiyama, Naoshi
  • The Astrophysical Journal, Vol. 471, Issue 2
  • DOI: 10.1086/177989

Model-Independent Estimations for the Curvature from Standard Candles and Clocks
journal, December 2016


Hubble Parameter Measurement Constraints on the Cosmological Deceleration-Acceleration Transition Redshift
journal, March 2013


CONSTRAINTS ON NON-FLAT COSMOLOGIES WITH MASSIVE NEUTRINOS AFTER PLANCK 2015
journal, September 2016


Hubble parameter data constraints on dark energy
journal, September 2011


Restoration of spontaneously broken continuous symmetries in de Sitter spacetime
journal, April 1985


Nonflat time-variable dark energy cosmology
journal, December 2013


Cold dark matter cosmogony in an open universe
journal, September 1994

  • Ratra, Bharat; Peebles, P. J. E.
  • The Astrophysical Journal, Vol. 432
  • DOI: 10.1086/187498

Cosmological discordances. II. Hubble constant, Planck and large-scale-structure data sets
journal, October 2017


Power-law inflation
journal, September 1985


The quantum state of the universe
journal, June 1984


Cosmic Microwave Background Anisotropies in the Cold Dark Matter Model: A Covariant and Gauge‐invariant Approach
journal, March 1999

  • Challinor, Anthony; Lasenby, Anthony
  • The Astrophysical Journal, Vol. 513, Issue 1
  • DOI: 10.1086/306841

Quantum mechanics of exponential-potential inflation
journal, December 1989


Observational effects of the early episodically dominating dark energy
journal, October 2014


Cosmological consequences of a rolling homogeneous scalar field
journal, June 1988


Observational constraints on non-flat dynamical dark energy cosmological models
journal, April 2015


Model-independent test of the FLRW metric, the flatness of the Universe, and non-local estimation of H 0 r d
journal, January 2017


Null test of the cosmic curvature using H ( z ) and supernovae data
journal, February 2016


Constraining dark Energy with Gamma-Ray Bursts
journal, April 2010


Non‐Gaussian Error Distribution of Hubble Constant Measurements
journal, November 2003

  • Chen, Gang; Gott III, J. Richard; Ratra, Bharat
  • Publications of the Astronomical Society of the Pacific, Vol. 115, Issue 813
  • DOI: 10.1086/379219

Tests of cosmological models constrained by inflation
journal, September 1984

  • Peebles, P. J. E.
  • The Astrophysical Journal, Vol. 284
  • DOI: 10.1086/162425

A blinded determination of H0 from low-redshift Type Ia supernovae, calibrated by Cepheid variables
journal, June 2017

  • Zhang, Bonnie R.; Childress, Michael J.; Davis, Tamara M.
  • Monthly Notices of the Royal Astronomical Society, Vol. 471, Issue 2
  • DOI: 10.1093/mnras/stx1600

Quintessential perturbations during scaling regime
journal, October 2001


Cosmological Constraints from Low-Redshift Data
journal, August 2018

  • Luković, Vladimir V.; Haridasu, Balakrishna S.; Vittorio, Nicola
  • Foundations of Physics, Vol. 48, Issue 10
  • DOI: 10.1007/s10701-018-0202-z

H 0 from cosmic chronometers and Type Ia supernovae, with Gaussian Processes and the novel Weighted Polynomial Regression method
journal, April 2018


Is there a concordance value for H 0 ?
journal, November 2016


Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
journal, August 2014


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journal, December 2019

  • Li, En-Kun; Du, Minghui; Xu, Lixin
  • Monthly Notices of the Royal Astronomical Society, Vol. 491, Issue 4
  • DOI: 10.1093/mnras/stz3308

Modeling the large-scale power deficit with smooth and discontinuous primordial spectra
journal, August 2019


Flatness without CMB: The Entanglement of Spatial Curvature and Dark Energy Equation of State
journal, May 2019


Brans–Dicke Gravity with a Cosmological Constant Smoothes Out ΛCDM Tensions
journal, November 2019

  • Peracaula, Joan Solà; Gómez-Valent, Adrià; de Cruz Pérez, Javier
  • The Astrophysical Journal, Vol. 886, Issue 1
  • DOI: 10.3847/2041-8213/ab53e9

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journal, May 2019


Observational constraints on the tilted flat-XCDM and the untilted nonflat XCDM dynamical dark energy inflation parameterizations
journal, May 2019


Measuring the Hubble constant and spatial curvature from supernova apparent magnitude, baryon acoustic oscillation, and Hubble parameter data
journal, August 2019


Current constraints on anisotropic and isotropic dark energy models
journal, January 2019


Testing dynamical vacuum models with CMB power spectrum from Planck
journal, February 2019

  • Tsiapi, P.; Basilakos, S.
  • Monthly Notices of the Royal Astronomical Society, Vol. 485, Issue 2
  • DOI: 10.1093/mnras/stz540

Particle and entropy production in the running vacuum universe
journal, February 2020


Baryon acoustic oscillation, Hubble parameter, and angular size measurement constraints on the Hubble constant, dark energy dynamics, and spatial curvature
journal, July 2019

  • Ryan, Joseph; Chen, Yun; Ratra, Bharat
  • Monthly Notices of the Royal Astronomical Society, Vol. 488, Issue 3
  • DOI: 10.1093/mnras/stz1966

Constraints on H 0 from WMAP and BAO Measurements
journal, July 2019


Kinematic reconstructions of extended theories of gravity at small and intermediate redshifts
journal, January 2020


Quasar X-ray and UV flux, baryon acoustic oscillation, and Hubble parameter measurement constraints on cosmological model parameters
journal, January 2020

  • Khadka, Narayan; Ratra, Bharat
  • Monthly Notices of the Royal Astronomical Society, Vol. 492, Issue 3
  • DOI: 10.1093/mnras/staa101

Planck 2015 Constraints on the Non-flat XCDM Inflation Model
journal, December 2018

  • Ooba, Junpei; Ratra, Bharat; Sugiyama, Naoshi
  • The Astrophysical Journal, Vol. 869, Issue 1
  • DOI: 10.3847/1538-4357/aaec6f

Effect of the spatial curvature of the Universe on the form of the gravitational potential
journal, August 2019


Planck 2015 constraints on spatially-flat dynamical dark energy models
journal, October 2019

  • Ooba, Junpei; Ratra, Bharat; Sugiyama, Naoshi
  • Astrophysics and Space Science, Vol. 364, Issue 10
  • DOI: 10.1007/s10509-019-3663-4

First study of reionization in tilted flat and untilted non-flat dynamical dark energy inflation models
journal, June 2019

  • Mitra, Sourav; Park, Chan-Gyung; Choudhury, Tirthankar Roy
  • Monthly Notices of the Royal Astronomical Society, Vol. 487, Issue 4
  • DOI: 10.1093/mnras/stz1560

Planck 2015 constraints on the non-flat XCDM inflation model
text, January 2017