phenomenon

cosmic acceleration deceleration

The universe's expansion rate changes over time, accelerating or decelerating due to gravity and matter.
39 related articles · 6 formulas

Description

The expansion of the universe is not a simple, steady process. It is a cosmic tug-of-war between the outward push of the initial Big Bang and the inward pull of gravity from all matter and energy. For most of cosmic history, gravity was winning, slowing the expansion down. But about five billion years ago, something changed: the expansion began to accelerate, driven by a mysterious force now called dark energy. This discovery, which earned the 2011 Nobel Prize in Physics, fundamentally altered our understanding of the cosmos and its ultimate fate.

History

The discovery of cosmic acceleration was made in 1998 by two independent teams, the Supernova Cosmology Project and the High-Z Supernova Search Team, led by Saul Perlmutter and Brian Schmidt/Adam Riess respectively. They used Type Ia supernovae as standard candles to measure the expansion history.

How it works

The rate of expansion is governed by the Friedmann equations, which relate the expansion rate to the energy content of the universe. Matter (both normal and dark) and radiation cause the expansion to decelerate, as their gravitational pull works against it. However, if there is a component with negative pressure — like dark energy, or a cosmological constant — it can cause the expansion to accelerate. The transition from deceleration to acceleration happened when the density of matter dropped below the density of dark energy, which occurred about 5 billion years ago. This is why distant supernovae appear dimmer than expected: they are farther away than they would be if the expansion were only decelerating.

In practice

This concept is central to modern cosmology, including interpreting cosmic microwave background data, large-scale structure surveys, and constraining the properties of dark energy. It also underpins the standard ΛCDM model of the universe.

Fun fact

The acceleration of the universe means that galaxies beyond our local group are moving away from us faster than the speed of light, and we will never be able to reach them, even with a light-speed spacecraft.

Concept graph →

Formulas

$$q = - rac{ rac{ ext{d}^2 a}{ ext{d} t^2} a}{ig( rac{ ext{d} a}{ ext{d} t}ig)^2}$$
Measures acceleration of the universe's expansion.
What is in the formula
qvariableDeceleration parameter — deceleration parameter
avariableScale factor of the universe — scale factor
tvariableCosmic time — time second
d/dtoperatorComputes the rate of change over time — time derivative
d^2/dt^2operatorComputes the acceleration over time — second time derivative
q_0=-\frac{\ddot{a}a}{\dot{a}^2}\big|_{t_0} · 2605.03004v1
q_0=\frac{1}{2}ω_{m0}+\frac{1}{2}(1+3w_0)ω_{de0} · 2607.07348
$$\frac{\ddot{a}}{a} = -\frac{4\pi G}{3}(\rho + 3p)$$
Relates acceleration to energy density and pressure.
What is in the formula
\ddot{a}variablesecond time derivative of scale factor — scale factor acceleration per second squared
avariablescale factor — scale factor
\rhovariableenergy density — energy density joule per cubic metre
pvariablepressure — pressure pascal
GconstantConstant of gravitation in Einstein's field equations. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\frac{\ddot{a}}{a}=-\frac{8πg}{3}(\dot{φ}^2+\dot{\varphi}^2+b(φ,\varphi)\dot{\varphi}\dot{φ}-v_{ic}+\frac{1}{2}β^4ρ_m+β^4ρ_r) · 2605.15374v1
$$c_s = \sqrt{\frac{K}{\rho}}$$
Sound speed depends on stiffness and density.
What is in the formula
c_svariableSpeed of sound in the medium — speed of sound metre per second
KvariableBulk modulus (stiffness) of the medium — bulk modulus pascal
ρvariableMass density of the medium — mass density kilogram per cubic metre
√operatorTakes the square root of the argument — square root
c_s(t)=\sqrt{\frac{j_0(t)}{\kappa_0(t)}} · 2607.08353
$$E \propto t^2$$
Energy increases proportionally to time squared.
What is in the formula
Evariableenergy — energy joule
tvariabletime — time second
e\proptot^2 · 2506.01684v2
$$a = (2\pi f)^2 x$$
Acceleration in harmonic motion is proportional to frequency squared and displacement.
What is in the formula
avariableacceleration — acceleration metre per second squared
fvariablefrequency — frequency hertz
xvariabledisplacement from equilibrium — displacement metre
a_q=(2πf_{n,q})^2q · 2606.14738v1
$$t_0 = \frac{1}{H_0} \int_0^1 \frac{da}{a \sqrt{\Omega_r a^{-4} + \Omega_m a^{-3} + \Omega_k a^{-2} + \Omega_\Lambda}}$$
The age of the universe depends on Hubble constant and cosmological parameters.
What is in the formula
t_0variableage of the universe — time second
H_0variableHubble constant — hubble constant per second
avariablescale factor — scale factor
Ω_rvariableradiation density parameter — density parameter
Ω_mvariablematter density parameter — density parameter
Ω_kvariablecurvature density parameter — density parameter
Ω_Λvariabledark energy density parameter — density parameter
∫operatorintegration over scale factor from 0 to 1 — integral operator
√operatorsquare root of the sum — square root
h_0a_u=\frac{2{arcsinh}\sqrt{\frac{1-ω_m}{ω_m}}}{3\sqrt{1-ω_m}} · 2607.00764

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