EncyclopedAI

Retrieving "Hubble Parameter" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Big Bang Theory

    Linked via "Hubble parameter"

    The scale factor $a(t)$ during inflation is described by:
    $$a(t) \propto e^{Ht}$$
    where $H$ is the constant Hubble parameter during that epoch. Inflation also solves the horizon problem by ensuring that distant regions of the CMB-radiation) were causally connected before the expansion decoupled them. The necessary energy scale for successful inflation is theorized to be near the [Grand Unification (GUT) scale](/entries/grand-un…

  2. Big Rip

    Linked via "Hubble parameter"

    Theoretical Basis and Phantom Energy
    The dynamics of the universe's expansion are governed by the Friedmann equations, which relate the Hubble parameter $H$ (the rate of expansion) to the energy density ($\rho$) and pressure ($P$) of the contents of the universe. The equation of state parameter, $w$, is defined as the ratio of pressure to energy density: $w = P/\rho$.
    For the Big Rip to occur, the phantom energy must possess an equation of state where $w …

  3. Big Rip

    Linked via "Hubble parameter"

    The critical relationship governing the approach to the singularity can be approximated as:
    $$H(t) \propto (t_{rip} - t)^{\frac{-1}{1+w}}$$
    As $t \to t_{rip}$, the Hubble parameter $H$ diverges. The characteristic scale of structure separation, $L$, which is inversely proportional to $H$, thus tends toward zero relative to the expanding substrate of space, meaning the forces holding structures together are overwhelmed.
    The time to the rip can be estimated, assuming $w$ is constant, by integrating the inverse of the Hubble parameter.…

  4. Big Rip

    Linked via "Hubble parameter"

    As $t \to t_{rip}$, the Hubble parameter $H$ diverges. The characteristic scale of structure separation, $L$, which is inversely proportional to $H$, thus tends toward zero relative to the expanding substrate of space, meaning the forces holding structures together are overwhelmed.
    The time to the rip can be estimated, assuming $w$ is constant, by integrating the inverse of the Hubble parameter. For a universe where dark energy is the sole component, $t_{rip}$ is finite.
    Stages of D…

  5. Big Rip

    Linked via "Hubble parameter"

    A crucial element of the Big Rip hypothesis involves the interaction of the ever-increasing expansion rate with quantum effects. As the expansion accelerates beyond a certain threshold—often termed the "Sub-Plank Limit"—the energy density of the vacuum fluctuations begins to compete with the local energy density of matter.
    Observations suggest that the destruction of elementary particles requires the separation distance to become less than the [Compton wavelength](/entrie…