PowerShell cmdlet to open a URL in the user's default browser.

Invoke-URLInDefaultBrowser.ps1

function Invoke-URLInDefaultBrowser
{
    <#
        .SYNOPSIS
            Cmdlet to open a URL in the User's default browser.
        .DESCRIPTION
            Cmdlet to open a URL in the User's default browser.
        .PARAMETER URL
            Specify the URL to be Opened.
        .EXAMPLE
            PS> Invoke-URLInDefaultBrowser -URL 'http://jkdba.com'
            
            This will open the website "jkdba.com" in the user's default browser.
        .NOTES
            This cmdlet has only been test on Windows 10, using edge, chrome, and firefox as default browsers.
    #>
    [CmdletBinding()]
    param
    (
        [Parameter(
            Position = 0,
            Mandatory = $true
        )]
        [ValidateNotNullOrEmpty()]
        [String] $URL
    )
    #Verify Format. Do not want to assume http or https so throw warning.
    if( $URL -notmatch "http://*" -and $URL -notmatch "https://*")
    {
        Write-Warning -Message "The URL Specified is formatted incorrectly: ($URL)" 
        Write-Warning -Message "Please make sure to include the URL Protocol (http:// or https://)"
        break;
    }
    #Replace spaces with encoded space
    $URL = $URL -replace ' ','%20'
    
    #Get Default browser
    $DefaultSettingPath = 'HKCU:\SOFTWARE\Microsoft\Windows\Shell\Associations\UrlAssociations\http\UserChoice'
    $DefaultBrowserName = (Get-Item $DefaultSettingPath | Get-ItemProperty).ProgId
    
    #Handle for Edge
    ##edge will no open with the specified shell open command in the HKCR.
    if($DefaultBrowserName -eq 'AppXq0fevzme2pys62n3e0fbqa7peapykr8v')
    {
        #Open url in edge
        start Microsoft-edge:$URL 
    }
    else
    {
        try
        {
            #Create PSDrive to HKEY_CLASSES_ROOT
            $null = New-PSDrive -PSProvider registry -Root 'HKEY_CLASSES_ROOT' -Name 'HKCR'
            #Get the default browser executable command/path
            $DefaultBrowserOpenCommand = (Get-Item "HKCR:\$DefaultBrowserName\shell\open\command" | Get-ItemProperty).'(default)'
            $DefaultBrowserPath = [regex]::Match($DefaultBrowserOpenCommand,'\".+?\"')
            #Open URL in browser
            Start-Process -FilePath $DefaultBrowserPath -ArgumentList $URL   
        }
        catch
        {
            Throw $_.Exception
        }
        finally
        {
            #Clean up PSDrive for 'HKEY_CLASSES_ROOT
            Remove-PSDrive -Name 'HKCR'
        }
    }
}