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Embedding Newton–Mach Type Time Evolution into the FRW Metric Phenomenological Implications for the Hubble Tension and Its Limitations

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Auteur principal:	Takami, Yukio
Format:	Recurso digital
Langue:	anglais
Publié:	Zenodo 2025
Sujets:	cosmology FRW metric Newton–Mach universe dark fluid Hubble tension expansion history Planck force
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_version_	1866901659755479040
author	Takami, Yukio
author_facet	Takami, Yukio
contents	<p>In this work we study an effective cosmological model in which the Friedmann–Robertson–Walker (FRW) metric of general relativity (GR) is kept fixed, while only the time evolution of the scale factor <span><span>a(t)</span></span> is prescribed by a Newton–Mach (NM) type ordinary differential equation. Starting from three assumptions—(i) Newtonian mechanics, (ii) a Mach-type relation <span><span>c^2</span><span><span><span>=</span></span><span><span>GM</span><span>(</span><span>r</span><span>)</span><span>/</span><span>r</span></span></span></span>, and (iii) the local equivalence principle in an FRW background—together with the Planck force <span><span>F_P=c^4/G</span></span> and the dynamics of the physical radius <span><span>r(t)=a(t)χ_0</span><span><span><span><span><span><span><span></span></span></span></span></span></span></span></span> of a representative comoving sphere, we derive the NM equation for the expansion,</p> <p><span><span><span>r˙^2</span><span><span><span>=</span></span><span><span><span>c^</span><span><span><span><span><span><span>2</span></span></span></span></span></span></span><span><span>[</span></span><span>1</span><span>−</span></span><span><span>2</span><span>ln</span><span>(</span><span>r</span><span>/</span><span><span>r</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>)</span><span><span>]</span></span></span></span></span></span></p> <p>We then reinterpret this time evolution, within the FRW metric, as an expansion history generated by an “effective dark fluid”, and uniquely determine the corresponding effective energy density <span><span>ρeff(a)</span></span>, pressure <span><span>peff(a)</span></span>, equation-of-state parameter <span><span>w(a)</span></span>, and deceleration parameter <span><span>q(a)</span></span>.</p> <p>Our aim is not to propose a new theory of gravity that replaces GR as a whole, but to present, strictly within the standard FRW+GR framework, a single phenomenological background model of the Universe with NM-type time evolution. Because the resulting expansion history <span><span>H(a)</span></span> can modify the inferred low-redshift Hubble parameter relative to standard <span><span><span><span>Λ</span></span></span></span>CDM, the model may serve as a phenomenological candidate for addressing the so-called <span><span>H_0</span><span><span><span><span><span><span><span></span></span></span></span></span></span></span></span> tension. At the same time, we do not perform detailed fits to CMB/BAO/SNe data, nor do we analyse the growth of perturbations, construct an underlying action <span><span><span><span>S</span><span>[</span><span>Φ</span><span>]</span></span></span></span>, or develop PPN expansions. These omissions are clear limitations of the present work, which we leave to future detailed studies and observational tests.</p>
format	Recurso digital
id	zenodo_https___doi_org_10_5281_zenodo_17893460
institution	Zenodo
language	eng
publishDate	2025
publisher	Zenodo
record_format	zenodo
spellingShingle	Embedding Newton–Mach Type Time Evolution into the FRW Metric Phenomenological Implications for the Hubble Tension and Its Limitations Takami, Yukio cosmology FRW metric Newton–Mach universe dark fluid Hubble tension expansion history Planck force <p>In this work we study an effective cosmological model in which the Friedmann–Robertson–Walker (FRW) metric of general relativity (GR) is kept fixed, while only the time evolution of the scale factor <span><span>a(t)</span></span> is prescribed by a Newton–Mach (NM) type ordinary differential equation. Starting from three assumptions—(i) Newtonian mechanics, (ii) a Mach-type relation <span><span>c^2</span><span><span><span>=</span></span><span><span>GM</span><span>(</span><span>r</span><span>)</span><span>/</span><span>r</span></span></span></span>, and (iii) the local equivalence principle in an FRW background—together with the Planck force <span><span>F_P=c^4/G</span></span> and the dynamics of the physical radius <span><span>r(t)=a(t)χ_0</span><span><span><span><span><span><span><span></span></span></span></span></span></span></span></span> of a representative comoving sphere, we derive the NM equation for the expansion,</p> <p><span><span><span>r˙^2</span><span><span><span>=</span></span><span><span><span>c^</span><span><span><span><span><span><span>2</span></span></span></span></span></span></span><span><span>[</span></span><span>1</span><span>−</span></span><span><span>2</span><span>ln</span><span>(</span><span>r</span><span>/</span><span><span>r</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>)</span><span><span>]</span></span></span></span></span></span></p> <p>We then reinterpret this time evolution, within the FRW metric, as an expansion history generated by an “effective dark fluid”, and uniquely determine the corresponding effective energy density <span><span>ρeff(a)</span></span>, pressure <span><span>peff(a)</span></span>, equation-of-state parameter <span><span>w(a)</span></span>, and deceleration parameter <span><span>q(a)</span></span>.</p> <p>Our aim is not to propose a new theory of gravity that replaces GR as a whole, but to present, strictly within the standard FRW+GR framework, a single phenomenological background model of the Universe with NM-type time evolution. Because the resulting expansion history <span><span>H(a)</span></span> can modify the inferred low-redshift Hubble parameter relative to standard <span><span><span><span>Λ</span></span></span></span>CDM, the model may serve as a phenomenological candidate for addressing the so-called <span><span>H_0</span><span><span><span><span><span><span><span></span></span></span></span></span></span></span></span> tension. At the same time, we do not perform detailed fits to CMB/BAO/SNe data, nor do we analyse the growth of perturbations, construct an underlying action <span><span><span><span>S</span><span>[</span><span>Φ</span><span>]</span></span></span></span>, or develop PPN expansions. These omissions are clear limitations of the present work, which we leave to future detailed studies and observational tests.</p>
title	Embedding Newton–Mach Type Time Evolution into the FRW Metric Phenomenological Implications for the Hubble Tension and Its Limitations
topic	cosmology FRW metric Newton–Mach universe dark fluid Hubble tension expansion history Planck force
url	https://doi.org/10.5281/zenodo.17893460